Statistical Properties of Dynamical Systems with Some Hyperbolicity

Statistical Properties of Dynamical Systems With Some Hyperbolicity

This paper is about the ergodic theory of attractors and conservative dynamical systems with hyperbolic properties on large parts (though not necessarily all) of their phase spaces. The main results are for discrete time systems. To put this work into context, recall that for Axiom A attractors the picture has been fairly complete since the 1970’s (see [S1], [B], [R2]). Since then much progress...

SOME ERGODIC PROPERTIES OF HYPER MV {ALGEBRA DYNAMICAL SYSTEMS

This paper provides a review on major ergodic features of semi-independent hyper MV {algebra dynamical systems. Theorems are presentedto make contribution to calculate the entropy. Particularly, it is proved that thetotal entropy of those semi-independent hyper MV {algebra dynamical systemsthat have a generator can be calculated with respect to their generator ratherthan considering all the par...

Statistical Properties of Nonequilibrium Dynamical Systems

We provide a general framework to study differentiability of SRB measures for one dimensional non-uniformly expanding maps. Our work covers systems that admit a finite SRB measure and it also covers systems that admit an infinite SRB measure. In particular, we obtain a linear response formula for both finite and infinite SRB measures. We apply our results to interval maps with a neutral fixed p...

On Statistical Properties of Dynamical Systems

Statistical properties of dynamical systems – simulation

We survey an area of recent development, relating dynamics to theoretical computer science. We discuss some aspects of the theoretical simulation and computation of the long term behavior of dynamical systems. We will focus on the statistical limiting behavior and invariant measures. We present a general method allowing the algorithmic approximation at any given accuracy of invariant measures. ...