Recurrence is a fundamental property of dynamical systems, which can be exploited to
characterise the system's behaviour in phase space. A powerful tool for their visualisation …

This paper reviews recent progress that has been made in the study of return times
distribution. We discuss recent results on the first return time for systems with various mixing …

The main objective of this book is to give a broad unified introduction to the study of
dimension and recurrence in hyperbolic dynamics. It includes a discussion of the …

This self-contained monograph presents a unified exposition of the thermodynamic
formalism and some of its main extensions, with emphasis on the relation to dimension …

Recurrence, Dimensions, and Lyapunov Exponents Page 1 623 0022-4715/02/0200-0623/0
© 2002 Plenum Publishing Corporation Journal of Statistical Physics, Vol. 106, Nos. 3/4 …

In this paper, we empirically show the dynamics of daily wavelet-filtered (denoised) S&P 500
returns (2000–2020) to consist of an almost equally divided combination of stochastic and …

Letˇ> 1 be a real number. LetTˇdenote theˇ-transformation on Œ0; 1. A cylinder of order n is
a set of real numbers in Œ0; 1 having the same first n digits in their ˇ-expansion. A cylinder is …

This note is concerned with the quantitative recurrence properties of beta dynamical system
([0, 1], Tβ) for general β> 1; the size of points with the prescribed recurrence rate is …

We study the dynamical Borel–Cantelli lemma for recurrence sets in a measure-preserving
dynamical system with a compatible metric d. We prove that under some regularity …

The classical theorem of Poincaré on recurrence only gives information of qualitative nature.
On the other hand it is clearly a matter of intrinsic difficulty and not of lack of interest that less …