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Description Topic: Computational methods, computability and computer aided proofs in dynamics with a special focus on statistical and ergodic properties. The understanding and forecasting of statistical properties of a dynamical model is a central topic in the modern theory of dynamical systems and in the applications. Computers already helps much in this understanding. This gives a strong motivation to the study of the theoretical limits of such computations and to the development of new methods and algorithms for the rigorous computation, where the reliability of the result is certified.

Speakers: Wael Bahsoun (Loughborough University) Stefano Galatolo (Università di Pisa) Walid Gooma (Egypt-Japan University of Science and Technology) Mathieu Hoyrup (INRIA, Nancy) Maurizio Monge (Universitade Federal do Rio de Janeiro) Isaia Nisoli (Universidade Federal do Rio de Janeiro) Cristobal Rojas (Universitade Andres Bello, Santiago) Michael Yampolsky (University of Toronto)

Material

School on Computation and Computability in Dynamics | (smr 2684)
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  • Monday, 21 July 2014
    • 10:00 - 17:00
      • 10:00 Opening Ceremony 15' ( Leonardo da Vinci Building Lecture Room B )
        Speaker: S. Luzzatto, S. Galatolo (ICTP, Universita' di Pisa)
      • 10:15 Presentation of participants 30' ( Leonardo da Vinci Building Lecture Room B )
      • 10:45 Introduction to the rigorous computation of invariant measures 1h0' ( Leonardo da Vinci Building Lecture Room B )
        Speaker: S. Galatolo (Universita' di Pisa)
      • 11:45 Discussion 45' ( Leonardo da Vinci Building Lecture Room B )
      • 12:30 Lunch Break 2h30' ( Leonardo da Vinci Building Lecture Room B )
      • 15:00 Implementing the rigorous computation of invariant measures I 1h0' ( Leonardo da Vinci Building Lecture Room B )
        Speaker: I. Nisoli and M. Monge (UFRJ, Brazil)
      • 16:00 Discussion 1h0' ( Leonardo da Vinci Building Lecture Room B )
  • Tuesday, 22 July 2014
    • 10:00 - 17:00
      • 10:00 Informal discussion. Spaces adapted to the transfer operator of Lorenz Like two dimensional maps 1h0' ( Leonardo da Vinci Building Lecture Room B )
        Speaker: R. Lucena (UFRJ, Brazil)
      • 11:00 Informal discussion. Rigorous computation of the invariant measure for Lorenz-like two dimensional maps 1h0' ( Leonardo da Vinci Building Lecture Room B )
        Speaker: S. Galatolo (Universita' di Pisa)
      • 12:00 Discussion 30' ( Leonardo da Vinci Building Lecture Room B )
      • 12:30 Lunch Break 2h30' ( Leonardo da Vinci Building Lecture Room B )
      • 15:00 Implementing the rigorous computation of invariant measures II 1h0' ( Leonardo da Vinci Building Lecture Room B )
        Speaker: I. Nisoli and M. Monge (UFRJ, Brazil)
      • 16:00 Discussion 1h0' ( Leonardo da Vinci Building Lecture Room B )
  • Wednesday, 23 July 2014
    • 09:00 - 17:00
      • 09:00 Self organized activities 2h0' ( Leonardo da Vinci Building Lecture Room B )
      • 11:00 Random dynamical systems approaches to noise-induced phenomena 1h0' ( Leonardo da Vinci Building Lecture Room B )
        Speaker: Y. Sato (Hokkaido University, Japan)
      • 12:00 Discussion 30' ( Leonardo da Vinci Building Lecture Room B )
      • 12:30 Lunch Break 2h30' ( Leonardo da Vinci Building Lecture Room B )
      • 15:00 The approximation of the spectrum via quantitative stability results, applications I 1h0' ( Leonardo da Vinci Building Lecture Room B )
        Speaker: W. Bahsoun (Loughborough University, UK)
      • 16:00 Discussion 1h0' ( Leonardo da Vinci Building Lecture Room B )
  • Thursday, 24 July 2014
    • 10:00 - 17:00
      • 10:00 Random decay of correlation and applications 1h0' ( Leonardo da Vinci Building Lecture Room B )
        Speaker: M. Stadlbauer (Universidade Federal de Bahia, Brazil)
      • 11:00 The approximation of the spectrum via quantitative stability results, applications II 1h0' ( Leonardo da Vinci Building Lecture Room B )
        Speaker: W. Bahsoun (Loughborough University, UK)
      • 12:00 Discussion 30' ( Leonardo da Vinci Building Lecture Room B )
      • 12:30 Lunch Break 2h30' ( Leonardo da Vinci Building Lecture Room B )
      • 15:00 The probability of stochastic dynamics in the real quadratic family 1h0' ( Leonardo da Vinci Building Lecture Room B )
        Speaker: S. Luzzatto and A. Golmakani (ICTP and University of Alagoas, Brazil)
      • 16:00 Discussion 1h0' ( Leonardo da Vinci Building Lecture Room B )
  • Friday, 25 July 2014
    • 09:00 - 17:00
      • 09:00 Self organized activities 3h30' ( Leonardo da Vinci Building Lecture Room B )
      • 12:30 Lunch Break 2h30' ( Leonardo da Vinci Building Lecture Room B )
      • 15:00 Self organized activities 1h0' ( Leonardo da Vinci Building Lecture Room B )
      • 16:00 Discussion 1h0' ( Leonardo da Vinci Building Lecture Room B )
  • Monday, 28 July 2014
    • 09:00 - 17:00
      • 09:00 Self organized activities 2h0' ( Leonardo da Vinci Building Lecture Room B )
      • 11:00 Introduction to computable analysis and computability in dynamics I 1h0' ( Leonardo da Vinci Building Lecture Room B )
        Speaker: L. C. Rojas Gonzalez and M. Hoyrup (University of Toronto, Canada and LORIA, France)
      • 12:00 Discussion 30' ( Leonardo da Vinci Building Lecture Room B )
      • 12:30 Lunch Break 2h30' ( Leonardo da Vinci Building Lecture Room B )
      • 15:00 Self organized activities 1h0' ( Leonardo da Vinci Building Lecture Room B )
      • 16:00 Discussion 1h0' ( Leonardo da Vinci Building Lecture Room B )
  • Tuesday, 29 July 2014
    • 09:00 - 17:30
      • 09:00 Self organized activities 2h0' ( Leonardo da Vinci Building Lecture Room B )
      • 11:00 Introduction to computable analysis and computability in dynamics II 1h0' ( Leonardo da Vinci Building Lecture Room B )
        Speaker: L. C. Rojas Gonzalez and M. Hoyrup (University of Toronto, Canada and LORIA, France)
      • 12:00 Discussion 30' ( Leonardo da Vinci Building Lecture Room B )
      • 12:30 Lunch Break 2h30' ( Leonardo da Vinci Building Lecture Room B )
      • 15:00 The Query Complexity of Real Functionals 1h30' ( Leonardo da Vinci Building Lecture Room B )
        Speaker: W. Gomaa (Egypt-Japan University of Science and Technology, Egypt)
      • 16:30 Informal Discussion. Uniformly ergodic results for discontinuous skew product transformations 1h0' ( Leonardo da Vinci Building Lecture Room B )
        Speaker: Z. Zhou (Chinese Academy of Sciences, Institute of Applied Mathematics)
  • Wednesday, 30 July 2014
    • 09:00 - 17:00
      • 09:00 Self organized activities 2h0' ( Leonardo da Vinci Building Lecture Room B )
      • 11:00 Computability and complexity of Julia sets 1h0' ( Leonardo da Vinci Building Lecture Room B )
        Speaker: M. Yampolsky (University of Toronto, Canada)
      • 12:00 Discussion 30' ( Leonardo da Vinci Building Lecture Room B )
      • 12:30 Lunch Break 2h30' ( Leonardo da Vinci Building Lecture Room B )
      • 15:00 Self organized activities 2h0' ( Leonardo da Vinci Building Lecture Room B )
  • Thursday, 31 July 2014
    • 09:00 - 17:00
      • 09:00 Self organized activities 2h0' ( Leonardo da Vinci Building Lecture Room B )
      • 11:00 Informal Discussion. The W map 1h30' ( Leonardo da Vinci Building Lecture Room B )
        Speaker: I. Nisoli (UFRJ, Brazil)
      • 12:30 Lunch Break 2h30' ( Leonardo da Vinci Building Lecture Room B )
      • 15:00 Self organized activities 1h0' ( Leonardo da Vinci Building Lecture Room B )
      • 16:00 Discussion 1h0' ( Leonardo da Vinci Building Lecture Room B )
  • Friday, 1 August 2014
    • 09:00 - 17:00
      • 09:00 Self organized activities 2h0' ( Leonardo da Vinci Building Lecture Room B )
      • 11:00 Informal Discussion. Python tutorial 1h30' ( Leonardo da Vinci Building Lecture Room B )
        Speaker: M. Monge (UFRJ, Brazil)
      • 12:30 Lunch Break 2h30' ( Leonardo da Vinci Building Lecture Room B )
      • 15:00 Self organized activities 1h0' ( Leonardo da Vinci Building Lecture Room B )
      • 16:00 Discussion 1h0' ( Leonardo da Vinci Building Lecture Room B )
  • Saturday, 2 August 2014
    • 09:00 - 12:30
      • 09:00 Self organized activities 3h0' ( Leonardo da Vinci Building Lecture Room B )
      • 12:00 Closing 30' ( Leonardo da Vinci Building Lecture Room B )
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