A PDE Approach to Finite Time Indicators in Ergodic Theory

DOI

10.1142/S1402925109000182How to use a DOI?

Keywords

Ergodic Theory; Lyapunov exponents; Fast Lyapunov Indicators; approximated first integrals; PDE viscous techniques

Abstract

For dynamical systems defined by vector fields over a compact invariant set, we introduce a new class of approximated first integrals based on finite time averages and satisfying an explicit first order partial differential equation. These approximated first integrals can be used as finite time indicators of the dynamics. On the one hand, they provide the same results on applications than other popular indicators; on the other hand, their PDE based definition — that we show robust under suitable perturbations — allows one to study them using the traditional tools of PDE environment. In particular, we formulate this approximating device in the Lyapunov exponents framework and we compare the operative use of them to the common use of the Fast Lyapunov Indicators to detect the phase space structure of quasi-integrable systems.

Copyright

© 2009 The Authors. Published by Atlantis Press and Taylor & Francis

Open Access

This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

Download article (PDF)

TY  - JOUR
AU  - Olga Bernardi
AU  - Franco Cardin
AU  - Massimiliano Guzzo
AU  - Lorenzo Zanelli
PY  - 2021
DA  - 2021/01/07
TI  - A PDE Approach to Finite Time Indicators in Ergodic Theory
JO  - Journal of Nonlinear Mathematical Physics
SP  - 195
EP  - 206
VL  - 16
IS  - 2
SN  - 1776-0852
UR  - https://doi.org/10.1142/S1402925109000182
DO  - 10.1142/S1402925109000182
ID  - Bernardi2021
ER  -