Document Type

Article

Department/Program

Physics

Journal Title

Chaos: An Interdiscipliary Journal of Nonlinear Science

Pub Date

9-2003

Publisher

American Institute of Physics

Volume

13

Issue

3

First Page

880

Abstract

We consider a dynamical system given by an area-preserving map on a two-dimensional phase plane and consider a one-dimensional line of initial conditions within this plane. We record the number of iterates it takes a trajectory to escape from a bounded region of the plane as a function along the line of initial conditions, forming an “escape-time plot.” For a chaotic system, this plot is in general not a smooth function, but rather has many singularities at which the escape time is infinite; these singularities form a complicated fractal set. In this article we prove the existence of regular repeated sequences, called “epistrophes,” which occur at all levels of resolution within the escape-time plot. (The word “epistrophe” comes from rhetoric and means “a repeated ending following a variable beginning.”) The epistrophes give the escape-time plot a certain self-similarity, called “epistrophic” self-similarity, which need not imply either strict or asymptotic self-similarity.

DOI

https://doi.org/10.1063/1.1598311

Download

Share Feedback

Included in

Physics Commons

Share

COinS