Rational integrals of 2-dimensional geodesic flows: New examples
Sign Up to like & getrecommendations! Published in 2021 at "Journal of Geometry and Physics"
DOI: 10.1016/j.geomphys.2021.104389
Abstract: The geodesic flow (1.1) is called completely integrable, if there exists an additional first integral, i.e. a function F (x, p) such that dF dt = {F,H} ≡ 0, and F,H are functionally independent a.e..… read more here.
Keywords: dimensional geodesic; geodesic flows; integrals dimensional; new examples ... See more keywords
On geodesic flows with symmetries and closed magnetic geodesics on orbifolds
Sign Up to like & getrecommendations! Published in 2020 at "Ergodic Theory and Dynamical Systems"
DOI: 10.1017/etds.2018.122
Abstract: Let $Q$ be a closed manifold admitting a locally free action of a compact Lie group $G$. In this paper, we study the properties of geodesic flows on $Q$ given by suitable G-invariant Riemannian metrics.… read more here.
Keywords: geodesic flows; closed magnetic; magnetic geodesics; flows symmetries ... See more keywords
Geodesic Flows Modelled by Expansive Flows
Sign Up to like & getrecommendations! Published in 2018 at "Proceedings of the Edinburgh Mathematical Society"
DOI: 10.1017/s0013091518000160
Abstract: Abstract Given a smooth compact surface without focal points and of higher genus, it is shown that its geodesic flow is semi-conjugate to a continuous expansive flow with a local product structure such that the… read more here.
Keywords: modelled expansive; expansive flows; flows modelled; geodesic flows ... See more keywords
Topological classification of integrable geodesic flows in a potential field on the torus of revolution
Sign Up to like & getrecommendations! Published in 2017 at "Lobachevskii Journal of Mathematics"
DOI: 10.1134/s1995080217060130
Abstract: A Liouville classification of integrable Hamiltonian systems which are the geodesic flows on 2-dimensional torus of revolution in a invariant potential field in the case of linear integral is obtained. This classification is obtained using… read more here.
Keywords: classification; potential field; classification integrable; torus revolution ... See more keywords