On the creation of conjugate points for thermostats

Fuente: arXiv
Salvato in:
Dettagli Bibliografici
Autori principali: Cuesta, Javier Echevarría, Reber, James Marshall
Natura: Preprint
Pubblicazione: 2025
Soggetti:
Accesso online:
Tags: Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
_version_ 1866908955690663936
author Cuesta, Javier Echevarría
Reber, James Marshall
author_facet Cuesta, Javier Echevarría
Reber, James Marshall
contents Let $(M, g)$ be a closed oriented Riemannian surface, and let $SM$ be its unit tangent bundle. We show that the interior in the $\mathcal{C}^2$ topology of the set of smooth functions $λ:SM\to \mathbb{R}$ for which the thermostat $(M, g, λ)$ has no conjugate points is a subset of those functions for which the thermostat is projectively Anosov. Moreover, we prove that if a reversible thermostat is projectively Anosov, then its non-wandering set contains no conjugate points.
format Preprint
id arxiv_https___arxiv_org_abs_2504_17153
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle On the creation of conjugate points for thermostats
Cuesta, Javier Echevarría
Reber, James Marshall
Dynamical Systems
Differential Geometry
37D30 (Primary) 37C10 (Secondary)
Let $(M, g)$ be a closed oriented Riemannian surface, and let $SM$ be its unit tangent bundle. We show that the interior in the $\mathcal{C}^2$ topology of the set of smooth functions $λ:SM\to \mathbb{R}$ for which the thermostat $(M, g, λ)$ has no conjugate points is a subset of those functions for which the thermostat is projectively Anosov. Moreover, we prove that if a reversible thermostat is projectively Anosov, then its non-wandering set contains no conjugate points.
title On the creation of conjugate points for thermostats
topic Dynamical Systems
Differential Geometry
37D30 (Primary) 37C10 (Secondary)
url https://arxiv.org/abs/2504.17153