-
Previous Article
Minimal yet measurable foliations
- JMD Home
- This Issue
-
Next Article
Loci in strata of meromorphic quadratic differentials with fully degenerate Lyapunov spectrum
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).
|
[1] |
Misha Bialy, Andrey E. Mironov. Rich quasi-linear system for integrable geodesic flows on 2-torus. Discrete & Continuous Dynamical Systems - A, 2011, 29 (1) : 81-90. doi: 10.3934/dcds.2011.29.81 |
[2] |
Eric Babson and Dmitry N. Kozlov. Topological obstructions to graph colorings. Electronic Research Announcements, 2003, 9: 61-68. |
[3] |
Antonio Rieser. A topological approach to spectral clustering. Foundations of Data Science, 2021 doi: 10.3934/fods.2021005 |
[4] |
Didier Bresch, Thierry Colin, Emmanuel Grenier, Benjamin Ribba, Olivier Saut. A viscoelastic model for avascular tumor growth. Conference Publications, 2009, 2009 (Special) : 101-108. doi: 10.3934/proc.2009.2009.101 |
[5] |
Michael Schmidt, Emmanuel Trélat. Controllability of couette flows. Communications on Pure & Applied Analysis, 2006, 5 (1) : 201-211. doi: 10.3934/cpaa.2006.5.201 |
[6] |
Elena Bonetti, Pierluigi Colli, Gianni Gilardi. Singular limit of an integrodifferential system related to the entropy balance. Discrete & Continuous Dynamical Systems - B, 2014, 19 (7) : 1935-1953. doi: 10.3934/dcdsb.2014.19.1935 |
[7] |
Elvise Berchio, Filippo Gazzola, Dario Pierotti. Nodal solutions to critical growth elliptic problems under Steklov boundary conditions. Communications on Pure & Applied Analysis, 2009, 8 (2) : 533-557. doi: 10.3934/cpaa.2009.8.533 |
[8] |
Manfred Einsiedler, Elon Lindenstrauss. On measures invariant under diagonalizable actions: the Rank-One case and the general Low-Entropy method. Journal of Modern Dynamics, 2008, 2 (1) : 83-128. doi: 10.3934/jmd.2008.2.83 |
[9] |
Charles Amorim, Miguel Loayza, Marko A. Rojas-Medar. The nonstationary flows of micropolar fluids with thermal convection: An iterative approach. Discrete & Continuous Dynamical Systems - B, 2021, 26 (5) : 2509-2535. doi: 10.3934/dcdsb.2020193 |
[10] |
Zhigang Pan, Chanh Kieu, Quan Wang. Hopf bifurcations and transitions of two-dimensional Quasi-Geostrophic flows. Communications on Pure & Applied Analysis, , () : -. doi: 10.3934/cpaa.2021025 |
[11] |
Hyeong-Ohk Bae, Hyoungsuk So, Yeonghun Youn. Interior regularity to the steady incompressible shear thinning fluids with non-Standard growth. Networks & Heterogeneous Media, 2018, 13 (3) : 479-491. doi: 10.3934/nhm.2018021 |
[12] |
A. Kochergin. Well-approximable angles and mixing for flows on T^2 with nonsingular fixed points. Electronic Research Announcements, 2004, 10: 113-121. |
2019 Impact Factor: 0.465
Tools
Metrics
Other articles
by authors
[Back to Top]