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Topological entropy of minimal geodesics and volume growth on surfaces
1. | Fakultät für Mathematik, Ruhr-Universität Bochum, 44780 Bochum, Germany, Germany |
2. | Institut de Mathématiques et de Sciences Physiques (IMSP), Université d’Abomey-Calavi 01 BP 613 Porto-Novo, Benin |
References:
[1] |
R. Bowen, Entropy-expansive maps,, Trans. Amer. Math. Soc., 164 (1972), 323.
doi: 10.1090/S0002-9947-1972-0285689-X. |
[2] |
V. Bangert, Mather sets for twist maps and geodesics on tori,, in Dynamics Reported, (1988), 1.
|
[3] |
G. Contreras, R. Iturriaga, G. P. Paternain and M. Paternain, Lagrangian graphs, minimizing measures and Mañé's critical values,, Geometric and Functional Analysis, 8 (1998), 788.
doi: 10.1007/s000390050074. |
[4] |
A. Freire and R. Mañé, On the entropy of the geodesic flow in manifolds without conjugate points,, Invent. Math., 69 (1982), 375.
doi: 10.1007/BF01389360. |
[5] |
E. Glasmachers, Characterization of Riemannian Metrics on $T^2$ with and without Positive Topological Entropy,, Ph.D thesis, (2007). Google Scholar |
[6] |
G. A. Hedlund, Geodesics on a two-dimensional Riemannian manifold with periodic coefficients,, Ann. of Math. (2), 33 (1932), 719.
doi: 10.2307/1968215. |
[7] |
A. Katok and B. Hasselblatt, Introduction to the Modern Theory of Dynamical Systems,, Encyclopedia of Mathematics and its Applications, (1995).
doi: 10.1017/CBO9780511809187. |
[8] |
W. Klingenberg, Geodätischer Fluss auf Mannigfaltigkeiten vom hyperbolischen Typ,, Invent. Math., 14 (1971), 63.
doi: 10.1007/BF01418743. |
[9] |
G. Knieper, Hyperbolic dynamics and riemannian geometry,, in Handbook of Dynamical Systems, (2002), 453.
doi: 10.1016/S1874-575X(02)80008-X. |
[10] |
A. Manning, Topological entropy for geodesic flows,, Annals of Math. (2), 110 (1979), 567.
doi: 10.2307/1971239. |
[11] |
M. Morse, A fundamental class of geodesics on any closed surface of genus greater than one,, Trans. Amer. Math. Soc., 26 (1924), 25.
doi: 10.1090/S0002-9947-1924-1501263-9. |
[12] |
P. Walters, An Introduction to Ergodic Theory,, Graduate Texts in Mathematics, (1982).
|
show all references
References:
[1] |
R. Bowen, Entropy-expansive maps,, Trans. Amer. Math. Soc., 164 (1972), 323.
doi: 10.1090/S0002-9947-1972-0285689-X. |
[2] |
V. Bangert, Mather sets for twist maps and geodesics on tori,, in Dynamics Reported, (1988), 1.
|
[3] |
G. Contreras, R. Iturriaga, G. P. Paternain and M. Paternain, Lagrangian graphs, minimizing measures and Mañé's critical values,, Geometric and Functional Analysis, 8 (1998), 788.
doi: 10.1007/s000390050074. |
[4] |
A. Freire and R. Mañé, On the entropy of the geodesic flow in manifolds without conjugate points,, Invent. Math., 69 (1982), 375.
doi: 10.1007/BF01389360. |
[5] |
E. Glasmachers, Characterization of Riemannian Metrics on $T^2$ with and without Positive Topological Entropy,, Ph.D thesis, (2007). Google Scholar |
[6] |
G. A. Hedlund, Geodesics on a two-dimensional Riemannian manifold with periodic coefficients,, Ann. of Math. (2), 33 (1932), 719.
doi: 10.2307/1968215. |
[7] |
A. Katok and B. Hasselblatt, Introduction to the Modern Theory of Dynamical Systems,, Encyclopedia of Mathematics and its Applications, (1995).
doi: 10.1017/CBO9780511809187. |
[8] |
W. Klingenberg, Geodätischer Fluss auf Mannigfaltigkeiten vom hyperbolischen Typ,, Invent. Math., 14 (1971), 63.
doi: 10.1007/BF01418743. |
[9] |
G. Knieper, Hyperbolic dynamics and riemannian geometry,, in Handbook of Dynamical Systems, (2002), 453.
doi: 10.1016/S1874-575X(02)80008-X. |
[10] |
A. Manning, Topological entropy for geodesic flows,, Annals of Math. (2), 110 (1979), 567.
doi: 10.2307/1971239. |
[11] |
M. Morse, A fundamental class of geodesics on any closed surface of genus greater than one,, Trans. Amer. Math. Soc., 26 (1924), 25.
doi: 10.1090/S0002-9947-1924-1501263-9. |
[12] |
P. Walters, An Introduction to Ergodic Theory,, Graduate Texts in Mathematics, (1982).
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