Evolution maps and symmetry. Issue 3 (4th March 2022)

• Record Type: Journal Article
• Authors: Barreira, Luis; Valls, Claudia
• Is Part Of: Journal of difference equations and applications. Volume 28:Issue 3(2022)
• Page Start: 355
• Page End: 384
• Publication Date: 2022-03-04
• Subjects: Evolution maps -- equivariance -- reversibility; Primary: 37D99; Difference equations -- Periodicals; 515.625
• DOI: 10.1080/10236198.2022.2042521
• Languages: English
• ISSNs: 1023-6198

Abstract

Abstract : We describe in detail how the symmetries of equivariance and reversibility induce corresponding properties for the stable and unstable invariant manifolds and for the stable and unstable foliations for any sufficiently small Lipschitz perturbation of a linear hyperbolic dynamics. This requires establishing first a faithful correspondence between the reversibility and equivariance properties of the original dynamics and corresponding properties for its evolution map.