Volume 20, Issue 1, April 2013, Pages 9 - 27
Convergence to the Time Average by Stochastic Regularization
Corresponding Authors
Olga Bernardi, Franco Cardin, Massimiliano Guzzo
Received 27 July 2012, Accepted 25 September 2012, Available Online 6 January 2021.
- DOI
- 10.1080/14029251.2013.792465How to use a DOI?
- Keywords
- Stochastic regularization techniques; approximated first integrals; Hamiltonian Perturbation Theory; Ergodic Theory
- Abstract
In Ergodic Theory it is natural to consider the pointwise convergence of finite time averages of functions with respect to the flow of dynamical systems. Since the pointwise convergence is too weak for applications to Hamiltonian Perturbation Theory, requiring differentiability, we first introduce regularized averages obtained through a stochastic perturbation of an integrable Hamiltonian flow, and then we provide detailed estimates. In particular, for a special vanishing limit of the stochastic perturbation, we obtain convergence even in a Sobolev norm taking into account the derivatives.
- Copyright
- © 2013 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/).
Cite this article
TY - JOUR AU - Olga Bernardi AU - Franco Cardin AU - Massimiliano Guzzo PY - 2021 DA - 2021/01/06 TI - Convergence to the Time Average by Stochastic Regularization JO - Journal of Nonlinear Mathematical Physics SP - 9 EP - 27 VL - 20 IS - 1 SN - 1776-0852 UR - https://doi.org/10.1080/14029251.2013.792465 DO - 10.1080/14029251.2013.792465 ID - Bernardi2021 ER -