Many dynamical systems behave similarly to a stochastic process; they are (very loosely) called "chaotic".
The course aims to illustrate several different techniques for studying and making precise such phenomena.
I particular, I will discuss the following properties:
invariant measures and decay of correlations
statistical stability and linear response
Central limit Theorem,
Large deviations, Invariance principle, extreme values statistics ...
Such concepts will be investigated by analyzing classes of systems of increasing complexity. More precisely:
Expanding maps (smooth and non-smooth)
Uniformly hyperbolic maps
Uniformly hyperbolic flows
Partially hyperbolic maps
non-uniformly hyperbolic systems
I will try to provide some notes for the material that cannot be easily found in print. Some of the topics can be found in:
Transfer operators in Hyperbolic Dynamics An introduction,
C.Liverani, M. Demers and N. Kiamari. 33 Colloquio Brasilero de Matematica. Editora do IMPA. pp.252 (2021)
Notes
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