NDLI: On the extendability of Noether’s integrals for orbifolds of constant negative curvature

Content Provider	Springer Nature Link
Author	Kozlov, Valery V.
Copyright Year	2016
Abstract	This paper is concerned with the problem of the integrable behavior of geodesics on homogeneous factors of the Lobachevsky plane with respect to Fuchsian groups (orbifolds). Locally the geodesic equations admit three independent Noether integrals linear in velocities (energy is a quadratic form of these integrals). However, when passing along closed cycles the Noether integrals undergo a linear substitution. Thus, the problem of integrability reduces to the search for functions that are invariant under these substitutions. If a Fuchsian group is Abelian, then there is a first integral linear in the velocity (and independent of the energy integral). Conversely, if a Fuchsian group contains noncommuting hyperbolic or parabolic elements, then the geodesic flow does not admit additional integrals in the form of a rational function of Noether integrals. We stress that this result holds also for noncompact orbifolds, when there is no ergodicity of the geodesic flow (since nonrecurrent geodesics can form a set of positive measure).
Starting Page	821
Ending Page	831
Page Count	11
File Format	PDF
ISSN	15603547
Journal	Regular and Chaotic Dynamics
Volume Number	21
Issue Number	7-8
e-ISSN	14684845
Language	English
Publisher	Pleiades Publishing
Publisher Date	2017-03-23
Publisher Place	Moscow
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Lobachevsky plane Fuchsian group orbifold Noether integrals Dynamical Systems and Ergodic Theory
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Statistical and Nonlinear Physics Mathematical Physics Mechanical Engineering Modeling and Simulation

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