Embedding of global attractors and their dynamics

2010/08/13 by de Moura, Eleonora Pinto, Robinson, James C., Sánchez-Gabites, Jaime J.
#Analysis of PDEs (math.AP) #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.1008.2329

Abstract

Using shape theory and the concept of cellularity, we show that if A is the global attractor associated with a dissipative partial differential equation in a real Hilbert space H and the set A-A has finite Assouad dimension d, then there is an ordinary differential equation in \mathbb R^m+1, with m >d, that has unique solutions and reproduces the dynamics on A. Moreover, the dynamical system generated by this new ordinary differential equation has a global attractor X arbitrarily close to LA, where L is a homeomorphism from A into \mathbb R^m+1.

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