Description
The Abdus Salam International Centre for Theoretical Physics (ICTP) is organizing a "School and Conference in Dynamical Systems".  The activity will be held from 20 July to 7 August 2015, in Trieste, Italy. It will be directed by S. Luzzatto (ICTP, Trieste, Italy), M. Viana (IMPA, Rio de Janeiro, Brazil) and J.-C. Yoccoz (Collège de France, Paris, France).

TOPICS

•	Chaotic dynamics: homoclinic bifurcations, attractors, generic systems, partial hyperbolicity and dominated splitting, Lorenz attractors.
•	Conservative dynamics: KAM and Aubry-Mather theories, diffusion in Hamiltonian systems, billiards, infinite dimensional systems, celestial mechanics.
•	Ergodic Theory: Sinai-Ruelle-Bowen measures, stochastic stability, Lyapunov exponents, linear cocycles, spectral theory of Schrodinger operators, recurrence and applications to Number Theory.
•	Geometric, algebraic, and topological aspects of Dynamics: smooth group actions, knots and braids, commutators.
•	One-dimensional dynamics: density of hyperbolicity, parametrized families of transformations, stochastic versus regular behavior.

During the two first weeks (20-31 July): courses on the following topics will be delivered:

Applications of homogeneous dynamics: from number theory to statistical mechanics
Jens Marklof (University of Bristol)/ Andreas Strömbergsson (Uppsala University)

Renormalization in low dimensional dynamics
Marco Martens (SUNY at Stony Brook)

Partially hyperbolic diffeomorphisms
Sylvain Crovisier (Université Paris 13)/ Rafael Potrie (CMAT)

The second and third week will be a conference. The invited speakers will include some of the best experts in the field as well as brillant young researchers. They will provide the participants with some of the most recent and most interesting perspectives for future research.
Go to day
  • Monday, 20 July 2015
    • 08:00 - 20:00
      Location: Leonardo Building - Budinich Lecture Hall
      • 08:00 Registration formalities 1h30' ( Leonardo Building - Lobby )
      • 09:30 Opening 15'
      • 09:45 Partially hyperbolic diffeomorphisms (part 1) 1h0'
        Speaker: Sylvain Crovisier & Rafael Potrie (Université Paris 13; CMAT)
        Material: Slides Video
      • 11:00 Renormalization in low dimensional dynamics (part 1) 1h0'
        Speaker: Marco Martens (SUNY at Stony Brook)
        Material: Slides Video
      • 12:00 Lunch 2h0' ( Leonardo Building - Cafeteria )
      • 14:00 Tutorials 2h0'
        Material: Exercise
      • 16:00 Coffee break 30'
      • 16:30 Partially hyperbolic diffeomorphisms (part 2) 1h0'
        Speaker: Sylvain Crovisier & Rafael Potrie (Université Paris 13; CMAT)
        Material: Video
      • 18:00 Welcome reception 2h0' ( Leonardo Building - Terrace )
  • Tuesday, 21 July 2015
    • 09:30 - 17:30
      Location: Leonardo Building - Budinich Lecture Hall
      • 09:30 Partially hyperbolic diffeomorphisms (part 3) 1h0'
        Speaker: Sylvain Crovisier & Rafael Potrie (Université Paris 13; CMAT)
        Material: Video
      • 11:00 Renormalization in low dimensional dynamics (part 2) 1h0'
        Speaker: Marco Martens (SUNY at Stony Brook)
        Material: Slides Video
      • 12:00 Lunch 2h0' ( Leonardo Building - Cafeteria )
      • 14:00 Tutorials 2h0'
        Material: Exercise
      • 16:00 Coffee break 30'
      • 16:30 Partially hyperbolic diffeomorphisms (part 4) 1h0'
        Speaker: Sylvain Crovisier & Rafael Potrie (Université Paris 13; CMAT)
        Material: Video
  • Wednesday, 22 July 2015
    • 09:30 - 17:30
      Location: Leonardo Building - Budinich Lecture Hall
      • 09:30 Partially hyperbolic diffeomorphisms (part 5) 1h0'
        Speaker: Sylvain Crovisier & Rafael Potrie (Université Paris 13; CMAT)
        Material: Video
      • 11:00 Renormalization in low dimensional dynamics (part 3) 1h0'
        Speaker: Marco Martens (SUNY at Stony Brook)
        Material: Slides Video
      • 12:00 Lunch 2h0' ( Leonardo Building - Cafeteria )
      • 14:00 Tutorials 2h0'
        Material: Exercise
      • 16:00 Coffee break 30'
      • 16:30 Partially hyperbolic diffeomorphisms (part 6) 1h0'
        Speaker: Sylvain Crovisier & Rafael Potrie (Université Paris 13; CMAT)
        Material: Video
  • Thursday, 23 July 2015
    • 09:30 - 17:30
      Location: Leonardo Building - Budinich Lecture Hall
      • 09:30 Partially hyperbolic diffeomorphisms (part 7) 1h0'
        Speaker: Sylvain Crovisier & Rafael Potrie (Université Paris 13; CMAT)
        Material: Video
      • 11:00 Renormalization in low dimensional dynamics (part 4) 1h0'
        Speaker: Marco Martens (SUNY at Stony Brook)
        Material: Slides Video
      • 12:00 Lunch 2h0' ( Leonardo Building - Cafeteria )
      • 14:00 Tutorials 2h0'
        Material: Exercise
      • 16:00 Coffee break 30'
      • 16:30 Partially hyperbolic diffeomorphisms (part 8) 1h0'
        Speaker: Sylvain Crovisier & Rafael Potrie (Université Paris 13; CMAT)
        Material: Video
  • Friday, 24 July 2015
    • 09:30 - 21:00
      Location: Leonardo Building - Budinich Lecture Hall
      • 09:30 Partially hyperbolic diffeomorphisms (part 9) 1h0'
        Speaker: Sylvain Crovisier & Rafael Potrie (Université Paris 13; CMAT)
        Material: Video
      • 11:00 Renormalization in low dimensional dynamics (part 5) 1h0'
        Speaker: Marco Martens (SUNY at Stony Brook)
        Material: Slides Video
      • 12:00 Lunch 2h0' ( Leonardo Building - Cafeteria )
      • 14:00 Partially hyperbolic diffeomorphisms (part 10) 1h0'
        Speaker: Sylvain Crovisier & Rafael Potrie (Université Paris 13; CMAT)
        Material: Video
      • 19:00 Social Dinner 2h0' ( Mignon Restaurant )
  • Monday, 27 July 2015
    • 08:30 - 17:05
      Location: Leonardo Building - Budinich Lecture Hall
      • 08:30 Registration formalities (Leonardo Building Hall) 30'
      • 09:00 Applications of homogeneous dynamics: from number theory to statistical mechanics (part 1) 1h0'
        Speaker: Jens Marklof & Andreas Strömbergsson (University of Bristol; Uppsala University)
        Material: Course outline Slides Video
      • 10:15 Applications of homogeneous dynamics: from number theory to statistical mechanics (part 2) 1h0'
        Speaker: Jens Marklof & Andreas Strömbergsson (University of Bristol; Uppsala University)
        Material: Video
      • 11:30 On the Finiteness of Attractors for piecewise $C^2$ Maps of the Interval 45'
        Speaker: Vilton Pinheiro (UFBA, Brazil)
        Material: Slides Video
      • 12:15 Lunch 1h30'
      • 13:45 Tutorial 1h30'
      • 15:15 Invariant pseudo-foliations for minimal homeomorphisms in dimension 2 45'
        Speaker: Alejandro Kocsard (UFF, Brazil)
        Material: Slides Video
      • 16:05 Renormalization in low dimensional dynamics (part 6) 1h0'
        Speaker: Marco Martens (SUNY at Stony Brook)
        Material: Slides Video
  • Tuesday, 28 July 2015
    • 09:00 - 18:00
      Location: Leonardo Building - Budinich Lecture Hall
      • 09:00 Applications of homogeneous dynamics: from number theory to statistical mechanics (part 3) 1h0'
        Speaker: Jens Marklof & Andreas Strömbergsson (University of Bristol; Uppsala University)
        Material: Video
      • 10:15 Renormalization in low dimensional dynamics (part 7) 1h0'
        Speaker: Marco Martens (SUNY at Stony Brook)
        Material: Slides Video
      • 11:30 Convergence of non conventional ergodic averages 45'
        Speaker: Idris Assani (UNC, USA)
        Material: Slides Video
      • 12:15 Lunch 1h30'
      • 13:45 Tutorial 1h30'
      • 15:15 Some properties of entropy for C^r interval maps 45'
        Speaker: David Burguet (University Pierre et Marie Curie)
        Material: Video
      • 16:05 Weak integrability for volume hyperbolic diffeomorphism in dimension 3 20'
        Speaker: Khadim War (ICTP/SISSA)
      • 16:25 Lyapunov exponents of linear cocycles - continuity via large deviations 20'
        Speaker: Silvius Klein (NTNU, Norway)
        Material: Slides
      • 17:00 Applications of homogeneous dynamics: from number theory to statistical mechanics (part 4) 1h0'
        Speaker: Jens Marklof & Andreas Strömbergsson (University of Bristol; Uppsala University)
        Material: Video
  • Wednesday, 29 July 2015
    • 09:00 - 18:20
      Location: Leonardo Building - Budinich Lecture Hall
      • 09:00 Applications of homogeneous dynamics: from number theory to statistical mechanics (part 5) 1h0'
        Speaker: Jens Marklof & Andreas Strömbergsson (University of Bristol; Uppsala University)
        Material: Hand-out Video
      • 10:15 Renormalization in low dimensional dynamics (part 8) 1h0'
        Speaker: Marco Martens (SUNY at Stony Brook)
        Material: Slides Video
      • 11:30 Almost reducibility for the linear quasi-periodic wave-equation 45'
        Speaker: Hakan Eliasson (Institut de Mathematiques de Jussieu)
        Material: Video
      • 12:15 Lunch 1h30'
      • 13:45 Tutorial 1h30'
      • 15:15 Three fundamental problems concerning codimension-one foliations 45'
        Speaker: Andrés Navas (USACH, Cile)
        Material: Video
      • 16:05 Ergodic theory for expanding thurston maps 20'
        Speaker: Zhiqiang Li (UCLA, USA)
        Material: Slides
      • 16:25 Symbolic Dynamics for Normally Hyperbolic Foliations 20'
        Speaker: Pablo Carrasco (ICMC, Brazil)
      • 17:00 Applications of homogeneous dynamics: from number theory to statistical mechanics (part 6) 1h0'
        Speaker: Jens Marklof & Andreas Strömbergsson (University of Bristol; Uppsala University)
        Material: Video
  • Thursday, 30 July 2015
    • 09:00 - 18:45
      Location: Leonardo Building - Budinich Lecture Hall
      • 09:00 Applications of homogeneous dynamics: from number theory to statistical mechanics (part 7) 1h0'
        Speaker: Jens Marklof & Andreas Strömbergsson (University of Bristol; Uppsala University)
        Material: Video
      • 10:15 Renormalization in low dimensional dynamics (part 9) 1h0'
        Speaker: Marco Martens (SUNY at Stony Brook)
        Material: Slides Video
      • 11:30 Measure and Smooth rigidity of lattice actions in low dimensions 45'
        Speaker: Federico Rodriguez-Hertz (Penn State, USA)
        Material: Video
      • 12:15 Lunch 1h30'
      • 13:45 Tutorial 1h30'
      • 15:15 The scaling mean and a Law of Large Permanents 45'
        Speaker: Mario Ponce (Pontificia Universidad Católica de Chile)
        Material: Slides
      • 16:05 Dynamical aspects of algebraic logic 20'
        Speaker: Giovanni Panti (University of Udine)
      • 16:25 Yang-Baxter Equation, Braided Groups and Braces 20'
        Speaker: Tatiana Gateva Ivanova (Bulgarian Academy of Sciences)
      • 17:00 Applications of homogeneous dynamics: from number theory to statistical mechanics (part 8) 1h0'
        Speaker: Jens Marklof & Andreas Strömbergsson (University of Bristol; Uppsala University)
        Material: Video
  • Friday, 31 July 2015
    • 09:00 - 15:15
      Location: Leonardo Building - Budinich Lecture Hall
      • 09:00 Applications of homogeneous dynamics: from number theory to statistical mechanics (part 9) 1h0'
        Speaker: Jens Marklof & Andreas Strömbergsson (University of Bristol; Uppsala University)
        Material: Video
      • 10:15 Renormalization in low dimensional dynamics (part 10) 1h0'
        Speaker: Marco Martens (SUNY at Stony Brook)
        Material: Slides Video
      • 11:30 Stochastic dynamics from a deterministic one 45'
        Speaker: Domokos Szasz (Hungarian Academy of Sciences)
        Material: Slides Video
      • 12:15 Lunch 1h30'
      • 13:45 Poster Session 1h30'
    • 15:15 - 18:00 Chair: Michael Benedicks (KTH)
      Location: Leonardo Building - Budinich Lecture Hall
      • 15:15 Diffusion of wind-tree billiards and Lyapunov exponents of the Hodge 45'
        Speaker: Anton Zorich (Université de Rennes 1)
        Material: Slides Video
      • 16:00 Statistical properties of the maximal entropy measure for partially hyperbolic attractors 20'
        Speaker: Armando de Castro Junior (UFBA)
        Material: Slides
      • 16:20 On the minimality of semigroup actions on the interval which are C1-close to the identity 20'
        Speaker: Katsutoshi Shinohara (Tokyo Metropolitan University)
      • 17:00 Applications of homogeneous dynamics: from number theory to statistical mechanics (part 10) 1h0'
        Speaker: Jens Marklof & Andreas Strömbergsson (University of Bristol; Uppsala University)
        Material: Video
    • 19:00 - 21:00
      • 19:00 Social dinner 2h0' ( Mignon Restaurant )
  • Monday, 3 August 2015
    • 09:00 - 14:00 Chair: Stefano Marmi (Scuola Normale Superiore di Pisa, Italy)
      • 09:00 Unique equilibrium states for geodesic flows in nonpositive curvature 45'
        Speaker: Keith Burns (Northwestern University, USA)
        Material: Slides Video
      • 10:00 The multiplicity of measures of maximuml entropy of smooth surface diffeomorphisms 45'
        Speaker: Jerome Buzzi (Département de Mathématiques d'Orsay, France)
        Material: Slides Video
      • 10:45 Coffee break 30'
      • 11:15 On quasiconformal (in)-compatibility of satellite copies of the Mandelbrot set 20'
        Speaker: Luciana L.A. Lomonaco (University of Sao Paulo, Brazil)
        Material: Slides
      • 11:45 On circle maps with a flat interval and Cherry flows 20'
        Speaker: Liviana Palmisano (IMPAN, Poland)
      • 12:05 Lunch break 1h55'
    • 14:00 - 18:00 Chair: Maria José Pacifico (UFRJ)
      • 14:00 Center-unstable foliations do not have compact leaves 45'
        Speaker: Jana Rodriguez-Hertz (Universidad de la Rep. Montevideo, Uruguay)
        Material: Video
      • 15:00 Holder regularity of solutions of the cohomological equation for interval exchange transformations 45'
        Speaker: Stefano Marmi (Scuola Normale Superiore di Pisa, Italy)
        Material: Video
      • 15:45 Coffee break 30'
      • 16:15 Regularity and bifurcation phenomena in simple families of maps 20'
        Speaker: Carlo Carminati (University of Pisa, Italy)
        Material: Slides
      • 16:45 Renormalization, substitutions and freezing phase transitions 20'
        Speaker: Renaud Leplaideur (Universite de Brest, France)
      • 17:15 Singular vector fields far away from horseshoe 45'
        Speaker: Shaobo Gan (Peking University, China)
        Material: Slides Video
  • Tuesday, 4 August 2015
    • 09:00 - 14:00 Chair: Keith Burns (Northwestern University, USA)
      • 09:00 Expansive models up to time preserving semi-conjugacy of geodesic 45'
        Speaker: Rafael Oswaldo Ruggiero Rodriguez (Pontificia Universidade Catolica do Rio de Janeiro, Brazil)
        Material: Video
      • 10:00 Recurrence on infinite cyclic covering 45'
        Speaker: Albert Fathi (ENS de Llyon, France)
        Material: Video
      • 10:45 Break 30'
      • 11:15 On the robustness of intermingled basins 45'
        Speaker: Raul Ures (Universidad de la Re. Uruguay)
        Material: Video
      • 12:00 Lunch break 2h0'
    • 14:00 - 18:00 Chair: Sebastian van Strien (Imperial College London, UK)
      • 14:00 Rempe model and Denjoy odometer for hedgehogs of complex quadratic polynomials 45'
        Speaker: Mitsuhiro Shishikura (Kyoto University, Japan)
        Material: Slides Video
      • 15:00 Geodesic flows on surfaces with non positive curvature that are Bernoulli 45'
        Speaker: Yuri Gomes Lima (University of Maryland, USA)
        Material: Article Video
      • 15:45 Break 30'
      • 16:15 Lyapunov spectrum for Henon-like maps at the first bifurcation 20'
        Speaker: Hiroki Takahashi (Keio University, Japan)
      • 16:45 Singularities accumulated by regular orbits 20'
        Speaker: Adriana Da Luz (Universidad de la Republica, Uruguay)
        Material: Slides
      • 17:15 Contracting Lorenz Attractor: statistical properties 45'
        Speaker: Maria Jose Pacifico (UFRJ, Brazil)
        Material: Slides Video
    • 19:00 - 21:00
      • 19:00 Social dinner 2h0' ( Mignon Restaurant )
  • Wednesday, 5 August 2015
    • 09:00 - 13:00 Chair: Henk Bruin (University of Vienna, Austria)
      • 09:00 On stability of elliptic fixed points and tori 45'
        Speaker: Bassam R. Fayad (Université Paris 13, France)
        Material: Video
      • 10:00 Perihelia reduction for the planetary problem, with applications 45'
        Speaker: Gabriella Pinzari (University of Napoli, Italy)
        Material: Slides Video
      • 10:45 Break 30'
      • 11:15 Eaton lenses, pseuo-integrable billiards and genericity along curves 45'
        Speaker: Corinna Ulcigrai (University of Bristol, UK)
        Material: Video
      • 12:00 Lunch break 1h0'
    • 13:00 - 18:00 Chair: Jerome Buzzi (Département de Mathématiques d'Orsay, France)
      • 13:00 Poster Session 1h0'
      • 14:00 Sharp mixing rates via inducing w.r.t. general return times 45'
        Speaker: Henk Bruin (University of Vienna, Austria)
        Material: Video
      • 15:00 Determinantal Point Processes and Their Quasi-Symmetries 45'
        Speaker: Alexander I.Bufetov (Steklov Mathematical Institute, Russian Federation)
        Material: Video
      • 15:45 Break 30'
      • 16:15 On parameter loci of the Hénon family 20'
        Speaker: Yutaka Ishii (Kyushu University, Japan)
        Material: Slides
      • 16:45 C^r-density of (non-uniform) hyperbolicity in partially hyperbolic systems 20'
        Speaker: Karina Daniela Marin (IMPA, Brazil)
      • 17:15 On the fractal geometry of horseshoes in arbitrary dimensions 45'
        Speaker: Carlos Moreira (IMPA, Brazil)
        Material: Slides Video
  • Thursday, 6 August 2015
    • 09:00 - 13:30 Chair: Juan Rivera-Letelier (Pontificia Universidad Católica de Chile, Chile)
      • 09:00 Fatou flowers and parabolic curves 45'
        Speaker: Marco Abate (University of Pisa, Italy)
        Material: Video
      • 10:00 Almost sure continuity along curves traversing the Mandelbrot set 45'
        Speaker: Michael Benedicks (Kungl Tekniska Hogskolan, Sweden)
        Material: Video
      • 10:45 Break 30'
      • 11:15 The ergodic properties of the Kusuoka measure 45'
        Speaker: Mark Pollicott (University of Warwick, UK)
        Material: Slides Video
      • 12:00 Lunch break 1h30'
    • 13:30 - 18:00 Chair: Konstantin Khanin (University of Toronto, Canada)
      • 13:30 Continuity of entropy map for nonuniformly hyperbolic systems 45'
        Speaker: Wenxiang Sun (Peking University, China)
        Material: Article Video
      • 14:30 Fictitious games: a class of piecewise smooth dynamical system with very interesting properties 45'
        Speaker: Sebastian van Strien (Imperial College London, UK)
        Material: Video
      • 15:15 Break 30'
      • 15:45 Takens' last problem and existence of non-trivial wandering domains 20'
        Speaker: Shin Kiriki (Tokai University, Japan)
        Material: Slides
      • 16:15 Generic dynamics on Wind-trees 20'
        Speaker: Alba Marina Malaga Sabogal (Aix-Marseille Universite, France)
        Material: Slides
      • 16:45 Holder Stability by Translations 20'
        Speaker: Javier Alexis Correa Mayobre (Universidade Federal Fluminense, Brazil)
      • 17:15 On error term of the prime periodic orbit theorem for expanding semiflows 45'
        Speaker: Masato Tsujii (Kyushu University, Japan)
        Material: Slides Video
  • Friday, 7 August 2015
    • 09:00 - 13:30 Chair: Marco Abate (University of Pisa, Italy)
      Location: Leonardo Building - Budinich Lecture Hall
      • 09:00 On rigidity theory for circle maps with breaks 45'
        Speaker: Konstantin Khanin (University of Toronto, Canada)
        Material: Video
      • 10:00 Geometric pressure in real and complex 1D dynamics via trees and via spanning sets 45'
        Speaker: Feliks Przytycki (Polish Academy of Sciences, Poland)
        Material: Video
      • 10:45 Break 30'
      • 11:15 C1-Genericity of Symplectic Diffeomorphisms and Lower Bounds for Topological Entropy 20'
        Speaker: Thiago Catalan (Federal University of Uberlandia, Brazil)
      • 11:45 The Lagrange Spectrum of some square-tiled surface 20'
        Speaker: Luca Marchese (Universite Paris 13, France)
        Material: Slides
      • 12:05 Group photo 10'
        Material: Photos
      • 12:15 Lunch break 1h15'
    • 13:30 - 17:00 Chair: Stefano Luzzatto (ICTP)
      Location: Leonardo Building - Budinich Lecture Hall
      • 13:30 Sensitive dependence of geometric Gibbs measures of one-dimensional maps 45'
        Speaker: Juan Rivera-Letelier (Pontificia Universidad Católica de Chile, Chile)
        Material: Video
      • 14:30 Equilibrium states for some partially hyperbolic maps 45'
        Speaker: Krerley Oliveira (Universidade Federal de Alagoas, Brazil)
        Material: Video
      • 15:15 Break 15'
      • 15:30 Complexity and Sturmian colorings of regular trees 20'
        Speaker: Dong Han Kim (Dongguk University, Rep. of Korea)
        Material: Slides
      • 15:50 Quasisymmetric rigidity of smooth maps 20'
        Speaker: Trevor Collin Clark (Imperial College London, UK)
      • 16:15 Building Thermodynamics For Non-uniformly Hyperbolic Maps 45'
        Speaker: Yakov Pesin (The Pennsylvania State University, USA)
        Material: Slides Video