Positive Topological Entropy for Magnetic Flows on Surfaces

Simple item page
dc.creatorMiranda, José Antônio Gonçalves
dc.date2006-06-29
dc.date2007-07-20
dc.date.accessioned2026-07-07T08:19:31Z
dc.date.available2026-07-07T08:19:31Z
dc.descriptionWe study the topological entropy of the magnetic flow on a closed riemannian surface. We prove that if the magnetic flow has a non-hyperbolic closed orbit in some energy set T^cM= E^{-1}(c), then there exists an exact $ C^\infty$-perturbation of the 2-form $ Ω$ such that the new magnetic flow has positive topological entropy in T^cM. We also prove that if the magnetic flow has an infinite number of closed orbits in T^cM, then there exists an exact C^1-perturbation of $ Ω$ with positive topological entropy in T^cM. The proof of the last result is based on an analog of Franks' lemma for magnetic flows on surfaces, that is proven in this work, and Mañé's techniques on dominated splitting. As a consequence of those results, an exact magnetic flow on S^2 in high energy levels admits a C^1-perturbation with positive topological entropy. In the appendices we show that an exact magnetic flow on the torus in high energy levels admits a $ C^\infty $-perturbation with positive topological entropy.
dc.description23 pages
dc.identifierhttps://arxiv.org/abs/math/0606740
dc.identifierhttp://arxiv.org/abs/math/0606740
dc.identifierNonlinearity 20 (2007) 2007-2031
dc.identifierdoi:10.1088/0951-7715/20/8/011
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/134790
dc.subjectDynamical Systems
dc.subject37B40; 37D30; 37J99
dc.titlePositive Topological Entropy for Magnetic Flows on Surfaces
dc.typetext

Files

Collections

arXiv