Issues of Chaos and Recurrence in Infinite Dimensions
Chaotic Dynamics
2009-11-17 v1 Analysis of PDEs
Dynamical Systems
Pattern Formation and Solitons
Abstract
Various issues with regard to chaos and recurrence in infinite dimensions are discussed. The doctrine we are trying to derive is that Sobolev spaces over bounded spatial domains do host chaos and recurrence, while Sobolev spaces over unbounded spatial domains are lack of chaos and recurrence. Local Sobolev spaces over unbounded spatial domains can host chaos and are natural phase spaces e.g. for fluid problems, but are very challenging to study.
Keywords
Cite
@article{arxiv.0911.2762,
title = {Issues of Chaos and Recurrence in Infinite Dimensions},
author = {Y. Charles Li},
journal= {arXiv preprint arXiv:0911.2762},
year = {2009}
}
Comments
Relevant manuscripts arXiv:0707.4458 and arXiv:0707.4456 [The Poincar\'e Recurrence Problem of Inviscid Incompressible Fluids, Asian J. Math, vol.13, no.1, 7-14, (2009). A Recurrence Theorem on the Solutions to the 2D Euler Equation Asian J. Math, vol.13, no.1, 1-6, (2009)]