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Description
An ICTP Meeting

The meeting belongs to a series of conferences organized since 2001 (Bedlewo, Poland (2023 and 2013), Luminy, France (2019 and 2011) Provo, USA (2017), Olmué, Chile (2015), Beijing, China (2009), Chicago, IL, USA (2006), Búzios, Brazil (2003), Evanston, USA (2001)). They have been instrumental for collaborations among the participants, furthering the subject and leading to new connections between different directions in the field.

Topics:
Partial hyperbolicity, Nonuniform hyperbolicity, Lyapunov exponents | Bifurcations: homoclinic tangencies, heterodimensional cycles | Typical phenomena: robustness, genericity, prevalence | Physical and Sinai-Ruelle-Bowen measures | Dimension theory, Thermodynamical Formalism | Statistical properties: decay of correlations, limit theorems | Symbolic dynamics, entropy, coding | Classification of dynamical systems, group actions and rigidity phenomena.

Further information:https://sites.google.com/view/beyonduniformhyperbolicity2025

Mini Courses:
  • Rigidity for generalized u-Gibbs measures: Aaron BROWN (Northwestern University, USA) and Federico RODRIGUEZ HERTZ (Penn State, USA)
  • Unstable entropy in smooth ergodic theory: Jérôme BUZZI (Université Paris Saclay, France) and Ali TAHZIBI (University of São Paulo, Brazil)
  • Complexity of classification of dynamical systems: Dominik KWIETNIAK (Jagiellonian University, Poland)

The related Beyond Uniform Hyperbolicity I: Higher rank actions, random walks and holomorphic dynamics (smr 4076) will take place the week before, from 2 to 6 June 2025.
Applications need to be made separately here: https://indico.ictp.it/event/10841/

Participants selected for both will receive a joint invitation letter.

Grants: A limited number of grants are available to support the attendance of selected participants, with priority given to participants from developing countries. There is no registration fee.

Material

Beyond Uniform Hyperbolicity II: Unstable entropy, generalized u-Gibbs measures and classification complexity | (smr 4157)
Go to day
  • Monday, 9 June 2025
    • 08:30 - 09:00
      • 08:30 Registration 30'
    • 09:00 - 17:10
      • 09:00 Rigidity for generalized u-Gibbs states - Part I 1h0'
        Speaker: Aaron BROWN (Northwestern University,USA) and Federico Juan RODRIGUEZ HERTZ (The Pennsylvania State University, USA)
      • 10:00 Break 40'
      • 10:40 Unstable entropy in smooth ergodic theory - Part I 1h0'
        Speaker: Jerome BUZZI (Paris-Saclay University, France) and Ali TAHZIBI (Sao Paolo University, Brazil)
        Material: Video
      • 11:50 Aperiodic classes of C1-generic diffeomorphisms 50'
        Speaker: Christian BONATTI (Bourgogne University, France)
        Material: Video
      • 13:00 Lunch Break 2h20'
      • 15:20 The Toolbox 50'
        Speaker: Dominik KWIETNIAK (Jagiellonian University in Kraków, Poland)
        Material: Video
      • 16:20 Thermodynamic formalism for coded shifts 50'
        Speaker: Tamara KUCHERENKO (City College, USA)
        Material: Video
    • 17:20 - 18:20 Lightning talks
      • 17:20 Existence of Measures of Maximal Entropy for a certain class of C1 Robustly transitive endomorphisms displaying critical points 10'
        Speaker: Elivan NERI LIMA (Federal University of Bahia, Brazil)
      • 17:30 A computer-assisted proof of the existence of blenders for a 3-dimensional Hénon-like family 10'
        Speaker: Natalia MC ALISTER CAFFAREL (Monash University, Australia)
      • 17:40 Unique equilibrium states for Viana maps with small potentials 10'
        Speaker: Kecheng LI (Tufts University Department of Mathematics, USA)
      • 17:50 The Variational Principle for Countable State Shift Spaces With Specification 10'
        Speaker: Amy SOMERS (University of California Santa Barbara, USA), Alexander PASCHAL (University of North Carolina, USA)
      • 18:00 Weakened Gibbs inequality for continuous potentials 10'
        Speaker: Arantha RANU (University of Victoria, Canada)
      • 18:10 A little hyperbolicity...”: Ergodicity of partially hyperbolic endomorphisms 10'
        Speaker: Audrey Tyler (Uruguay)
    • 19:00 - 21:00
      • 19:00 Welcome Reception 2h0' ( Leonardo Building Terrace ) 
        All Participants are cordially invited to the Welcome Reception
  • Tuesday, 10 June 2025
    • 09:00 - 18:10
      • 09:00 Unstable entropy in smooth ergodic theory - Part II 1h0'
        Speaker: Jerome BUZZI (Paris-Saclay University, France) and Ali TAHZIBI (Sao Paolo University, Brazil)
        Material: Video
      • 10:00 Break / Posters 40'
      • 10:40 Rigidity for generalized u-Gibbs states - Part II 1h0'
        Speaker: Aaron BROWN (Northwestern University,USA) and Federico Juan RODRIGUEZ HERTZ (The Pennsylvania State University, USA)
      • 11:50 Projections of self-affine fractals 50'
        Speaker: Cagri SERT (University of Warwick, UK)
        Material: Video
      • 13:00 Lunch Break 2h20'
      • 15:20 Lyapunov spectrum of volume-preserving partially hyperbolic maps 50'
        Speaker: Karina Daniela MARIN (Federal University of Minas Gerais, Brazil)
        Material: Video
      • 16:20 A dichotomy for conservative partially hyperbolic diffeomorphisms: hyperbolicity versus nonhyperbolic measures 50' ( Euler-Lagrange seminar room )
        Speaker: Jinhua ZHANG (Beihang University, China)
      • 16:20 Generalized u-Gibbs measures for Coo diffeomorphisms 50' ( Leonardo Building - Budinich Lecture Hall )
        Speaker: Snir BEN OVADIA (Pennsylvania State University, USA)
      • 17:20 Asymptotic counting of surfaces in negatively curved three manifolds 50' ( Leonardo Building - Budinich Lecture Hall )
        Speaker: Sebastien ALVAREZ (University of the Republic, Uruguay)
      • 17:20 Horocyclic flows in nonpositive curvature 50' ( Euler-Lagrange seminar room )
        Speaker: Sergi BURNIOL CLOTET (University of the Republic, Uruguay)
  • Wednesday, 11 June 2025
    • 09:00 - 17:20
      • 09:00 The Scoreboard 1h0'
        Speaker: Dominik KWIETNIAK (Jagiellonian University in Kraków, Poland)
        Material: Video
      • 10:00 Group Photo 5'
      • 10:05 Break 35'
      • 10:40 Unstable entropy in smooth ergodic theory - Part III 1h0'
        Speaker: Jerome BUZZI (Paris-Saclay University, France) and Ali TAHZIBI (Sao Paolo University, Brazil)
        Material: Video
      • 11:50 K and Bernoulli properties in smooth dynamical systems 50'
        Speaker: Adam KANIGOWSKI (University of Maryland, USA)
        Material: Video
      • 13:00 Lunch Break 2h20'
      • 15:20 Free afternoon 2h0'
  • Thursday, 12 June 2025
    • 09:00 - 18:10
      • 09:00 Unstable entropy in smooth ergodic theory - Part IV 1h0'
        Speaker: Jerome BUZZI (Paris-Saclay University, France) and Ali TAHZIBI (Sao Paolo University, Brazil)
        Material: Video
      • 10:00 Break / Posters 40'
      • 10:40 Rigidity for generalized u-Gibbs states - Part III 1h0'
        Speaker: Aaron BROWN (Northwestern University,USA) and Federico Juan RODRIGUEZ HERTZ (The Pennsylvania State University, USA)
      • 11:50 Positive entropy actions by higher rank lattices 50'
        Speaker: Homin LEE (Northwestern University, Korea)
        Material: Video
      • 13:00 Lunch Break 2h20'
      • 15:20 On fibered rotation numbers of one-parameter families of cocycles 50'
        Speaker: Anton GORODETSKI (University of California, USA)
        Material: Video
      • 16:20 Computer-assisted proof of robust transitivity in dimension 3 using blenders 50' ( Euler-Lagrange seminar room )
        Speaker: Marisa DOS REIS CANTARINO (Monash University, Australia)
      • 16:20 A Version of Oseledets Theorem for Proximal RDSs on the Circle 50' ( Leonardo Building - Budinich Lecture Hall )
        Speaker: Graccyela Rosybell SALCEDO PIRELA (École Polytechnique, France)
      • 17:20 Rotational Axiom A homeomorphisms for higher genus surfaces 50' ( Euler-Lagrange seminar room )
        Speaker: Pierre-Antoine Hugues Marie GUIHENEUF (MJ-PRG - Sorbonne University, France)
      • 17:20 Rigidity of transitive Anosov flows in dimension 3 50' ( Leonardo Building - Budinich Lecture Hall )
        Speaker: Martin Pierre Marie LEGUIL (École Polytechnique, France)
  • Friday, 13 June 2025
    • 09:00 - 16:10
      • 09:00 Rigidity for generalized u-Gibbs states - Part IV 1h0'
        Speaker: Aaron BROWN (Northwestern University,USA) and Federico Juan RODRIGUEZ HERTZ (The Pennsylvania State University, USA)
        Material: Video
      • 10:00 Break 40'
      • 10:40 The Action 1h0'
        Speaker: Dominik KWIETNIAK (Federal Univesity of Rio de Janeiro, Brazil)
        Material: Video
      • 11:50 An extension of Katok non-stationary normal coordinate along one dimensional invariant manifold 50'
        Speaker: Masato TSUJII (Kyushu University, Japan)
        Material: Video
      • 13:00 Lunch Break 2h20'
      • 15:20 On the stability and instability of elliptic equilibria and invariant quasi-periodic tori of real analytic Hamiltonians 50'
        Speaker: Bassam FAYAD (University of Maryland, USA)
        Material: Video
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