Dynamics of Partial Differential Equations
Volume 8 (2011)
Issues of chaos and recurrence in infinite dimensions
Pages: 69 – 77
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.
chaos, recurrence, fluids, soliton equation, Hamiltonian system
2010 Mathematics Subject Classification
Primary 35-xx, 37-xx. Secondary 76Xxx.