We consider the number of Bowen sets necessary to cover a large measure subset of the phase space. This introduces some complexity indicator characterizing different kinds of (weakly) chaotic dynamics. Since in many systems its value is given by a sort of local entropy, this indicator is quite simple to calculate. We give some examples of calculations in nontrivial systems (e.g., interval exchanges and piecewise isometries) and a formula similar to that of Ruelle-Pesin, relating the complexity indicator to some initial condition sensitivity indicators playing the role of positive Lyapunov exponents.

Metric complexity for weakly chaotic systems

GALATOLO, STEFANO
2007

Abstract

We consider the number of Bowen sets necessary to cover a large measure subset of the phase space. This introduces some complexity indicator characterizing different kinds of (weakly) chaotic dynamics. Since in many systems its value is given by a sort of local entropy, this indicator is quite simple to calculate. We give some examples of calculations in nontrivial systems (e.g., interval exchanges and piecewise isometries) and a formula similar to that of Ruelle-Pesin, relating the complexity indicator to some initial condition sensitivity indicators playing the role of positive Lyapunov exponents.
Galatolo, Stefano
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11568/113169
 Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 1
  • ???jsp.display-item.citation.isi??? 1
social impact