A connecting theorem for geodesic flows on the 2-torus
@inproceedings{Klempnauer2021ACT,
title={A connecting theorem for geodesic flows on the 2-torus},
author={Stefan Klempnauer},
year={2021}
}We use a result of J. Mather on the existence of connecting orbits for compositions of monotone twist maps of the cylinder to prove the existence of connecting geodesics on the unit tangent bundle ST 2 of the 2-torus in regions without invariant tori. The author thanks the SFB CRC/TRR 191 Symplectic Structures in Geometry, Algebra and Dynamics of the DFG and the Ruhr-University Bochum for the funding of his research.
References
SHOWING 1-7 OF 7 REFERENCES
Tonelli Lagrangians on the 2-torus : global minimizers , invariant tori and topological entropy
- Mathematics
- 2013
We study the Euler-Lagrange flow of a Tonelli Lagrangian on the 2-torus T2 in a fixed energy level E ⊂ TT2 strictly above Mañé’s strict critical value. Our results include • the structure of globally…
An Introduction to Riemann-Finsler Geometry
- Mathematics
- 2000
One Finsler Manifolds and Their Curvature.- 1 Finsler Manifolds and the Fundamentals of Minkowski Norms.- 1.0 Physical Motivations.- 1.1 Finsler Structures: Definitions and Conventions.- 1.2 Two…
Surface transformations and their dynamical applications
- Mathematics
- 1922
A state of motion in a dynamical system with two degrees of freedom depends on two space and two velocity coiirdinates, and thus may be represented by means of a point in space of four dimensions.…
An Introduction to Riemann-Finsler
- 2000
Symplectic Twist Maps, World
- Scientific Publishing,
- 2001