Dynamically defined recurrence dimension

Petr Kůrka; Vincent Penné; Sandro Vaienti

doi:10.3934/dcds.2002.8.137

Article Contents

2002, Volume 8, Issue 1: 137-146. Doi: 10.3934/dcds.2002.8.137

This issue Previous Article Deterministic and random aspects of porosities Next Article Global bifurcation structure of stationary solutions for a Lotka-Volterra competition model

Dynamically defined recurrence dimension

1.
Faculty of Mathematics and Physics, Charles University in Prague
2.
PHYMAT, Université de Toulon et du Var, Centre de Physique Théorique, Luminy

Received: July 31, 2000

Revised: June 30, 2001

Published: December 2001

Abstract Related Papers Cited by

Abstract

We modify the idea of a previous article [8] and introduce polynomial and exponential dynamically defined recurrence dimensions, topological invariants which express how the Poincaré recurrence time of a set grows when the diameter of the set shrinks. We introduce also the concept of polynomial entropy which applies in the case that topological entropy is zero and complexity function is polynomial. We compare recurrence dimensions with topological and polynomial entropies, evaluate recurrence dimensions of Sturmian subshifts and show some examples with Toeplitz subshifts.

Keywords:

Mathematics Subject Classification: 37B20, 37B40, 37C45, 37B10.

Citation:

Article Metrics

HTML views() PDF downloads(147) Cited by(0)

Dynamically defined recurrence dimension

Abstract

Access History

Article Metrics

Access History

Other Articles By Authors

Catalog

Dynamically defined recurrence dimension

Abstract

Access History

SHARE

Article Metrics

Access History

Other Articles By Authors

Catalog

Export File

Citation

Format

Content