Issues of Chaos and Recurrence in Infinite Dimensions

Details Issues of Chaos and Recurrence in Infinite Dimensions Issues of Chaos and Recurrence in Infinite Dimensions

2009-11-16

arxiv.org/abs/0911.2762v1

Nonlinear Sciences

Chaotic Dynamics

Relevant manuscripts arXiv:0707.4458 and arXiv:0707.4456 [The Poincar\'e Recurrence Problem of Inviscid Incompressible Fluids,

Scientific paper

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.

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