Dynamics of Partial Differential Equations

Volume 8 (2011)

Number 1

Issues of chaos and recurrence in infinite dimensions

Pages: 69 – 77

DOI: http://dx.doi.org/10.4310/DPDE.2011.v8.n1.a5

Author

Y. Charles Li (Department of Mathematics, University of Missouri, Columbia, Missouri)

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

chaos, recurrence, fluids, soliton equation, Hamiltonian system

2010 Mathematics Subject Classification

Primary 35-xx, 37-xx. Secondary 76Xxx.

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