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School on probabilistic aspects of hyperbolic dynamical systems

08/12/2024 - 08/16/2024
Big Lecture Hall, Rényi Institute


The school aims to familiarize young researchers with some of the most recent advances in the theory of ergodic and statistical properties of hyperbolic dynamical systems. Special emphasis will be put on the potential of the combination of various geometric, probabilistic and spectral methods, the description of systems with multiple time scales and further time-dependent phenomena.


Mark Demers: Entropy and topological pressure for Sinai billiards

Lecture 1: Complexity bounds and growth lemmas
Lecture 2: Banach spaces for billiards 
Lecture 3: MME for finite horizon Sinai billiard

Dmitry Dolgopyat: Limit theorems for non-stationary dynamical systems 

Lecture 1: Sequential Ruelle-Perron-Frobenius Theorem
Lecture 2: Martingale coboundary decomposition 
Lecture 3: Local limit theorem 

Gary Froyland: Finite-time coherent dynamics and applications

Lecture 1: Diffusive transfer operators and finite-time mixing
Lecture 2: Dynamic isoperimetry, the dynamic Laplacian, and finite-time coherent sets
Lecture 3: An inflated dynamic Laplacian and the birth/death of coherent dynamics

Carlangelo Liverani: Projective cones and applications to dispersing billiards

Lecture 1:  Introduction to hyperbolic billiards (hyperbolicity, collision map, foliations, ergodicity) 
Lecture 2:  Banach spaces, cones and statistical properties for simple systems 
Lecture 3:  Cones for Billiards  and applications


Link to the registration page:

Registration is open until 3 August 2024. After registration, we will notify you within two weeks whether your application has been accepted.

The sooner you register, the better. Please note that applications for financial support for accommodation are closed much earlier - see below. The school takes place during the top touristic season in Budapest, so accommodation prices can be expected to increase dramatically with time.


Limited financial support for accommodation is available for students and postdocs. Accommodation is provided in 2-bed rooms. Applications should be submitted as soon as possible but not later than March 31, 2024 (DEADLINE EXTENDED!). Applications should be sent by email to including CV and list of publications. Applicants should also arrange for a short letter of recommendation to be sent to the same email address by a faculty member, preferably the advisor/mentor. Please note that those who are supported are expected to attend the whole event. Accommodation is normally supported from Sunday to Saturday at most.

If you don't need financial support, but you would like our administration to help you with booking (at possibly discounted prices), please write to Mrs. Ildikó Bogáti:


Apart from the above support in accommodation, we cannot cover local expenses.



Peter Balint (BME)
Peter Nandori (Yeshiva University)
Francoise Pene (University Brest)
Domokos Szasz (BME)
Imre Peter Toth (BME)

Invited Speakers

Mark Demers (Fairfield University, USA)
Dmitry Dolgopyat (University of Maryland, USA)
Gary Froyland (UNSW, Australia)
Carlangelo Liverani (Univ. of Roma Tor Vergata, Italy)