Local perturbations of conservative C1 diffeomorphisms. (17th August 2017)

• Record Type: Journal Article
• Authors: Buzzi, Jérôme; Crovisier, Sylvain; Fisher, Todd
• Is Part Of: Nonlinearity. Volume 30:Number 9(2017:Sep.)
• Page Start: 3613
• Page End: 3636
• Publication Date: 2017-08-17
• Subjects: dominated splitting -- conservative diffeomorphisms -- perturbation; 37C20 -- 37C25 -- 37C29 -- 37J10; Nonlinear theories -- Periodicals; Mathematical analysis -- Periodicals; Mathematical analysis; Nonlinear theories; Periodicals; 515
• DOI: 10.1088/1361-6544/aa803f
• Languages: English
• ISSNs: 0951-7715

Abstract

Abstract: A number of techniques have been developed to perturb the dynamics of C 1 -diffeomorphisms and to modify the properties of their periodic orbits. For instance, one can locally linearize the dynamics, change the tangent dynamics, or create local homoclinic orbits. These techniques have been crucial for the understanding of C 1 dynamics, but their most precise forms have mostly been shown in the dissipative setting. This work extends these results to volume-preserving and especially symplectic systems. These tools underlie our study of the entropy of C 1 -diffeomorphisms in Buzzi et al (2016 (arXiv:1606.01765)). We also give an application to the approximation of transitive invariant sets without genericity assumptions.