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Open problems and questions about geodesics
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KEITH BURNS, VLADIMIR S. MATVEEV
Journal:

Ergodic Theory and Dynamical Systems / Volume 41 / Issue 3 / March 2021

Published online by Cambridge University Press:

06 December 2019, pp. 641-684

Print publication:

March 2021
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The paper surveys open problems and questions related to geodesics defined by Riemannian, Finsler, semi-Riemannian and magnetic structures on manifolds. It is an extended report on problem sessions held during the International Workshop on Geodesics in August 2010 at the Chern Institute of Mathematics in Tianjin.

Erratum to the Paper “A Lower Bound for the Length of Closed Geodesics on a Finsler Manifold”
Wei Zhao
Journal:

Canadian Mathematical Bulletin / Volume 57 / Issue 1 / 14 March 2014

Published online by Cambridge University Press:

20 November 2018, p. 209

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14 March 2014
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We correct two clerical errors made in the paper ”A Lower Bound for the Length of Closed Geodesics on a Finsler Manifold”.

A Lower Bound for the Length of Closed Geodesics on a Finsler Manifold
Wei Zhao
Journal:

Canadian Mathematical Bulletin / Volume 57 / Issue 1 / 14 March 2014

Published online by Cambridge University Press:

20 November 2018, pp. 194-208

Print publication:

14 March 2014
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In this paper, we obtain a lower bound for the length of closed geodesics on an arbitrary closed Finsler manifold.

Pairs of periodic orbits with fixed homology difference
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- Dynamical systems with hyperbolic behavior
- Smooth dynamical systems: general theory
Morten S. Risager, Richard Sharp
Journal:

Proceedings of the Edinburgh Mathematical Society / Volume 53 / Issue 3 / October 2010

Published online by Cambridge University Press:

12 August 2010, pp. 799-808
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We obtain an asymptotic formula for the number of pairs of closed orbits of a weak-mixing transitive Anosov flow whose homology classes have a fixed difference.

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