-
Previous Article
Non--autonomous and random attractors for delay random semilinear equations without uniqueness
- DCDS Home
- This Issue
-
Next Article
Axiom a systems without sinks and sources on $n$-manifolds
Growth of the number of geodesics between points and insecurity for Riemannian manifolds
1. | Department of Mathematics, Northwestern University, Evanston, IL 60208-2730 |
2. | IMPA, Estrada Dona Castorina 110, Rio de Janeiro 22460-320, Brazil |
We derive from this that a compact Riemannian manifold with no conjugate points whose geodesic flow has positive topological entropy is totally insecure: the geodesics between any pair of points cannot be blocked by a finite number of point obstacles.
[1] |
Eva Glasmachers, Gerhard Knieper, Carlos Ogouyandjou, Jan Philipp Schröder. Topological entropy of minimal geodesics and volume growth on surfaces. Journal of Modern Dynamics, 2014, 8 (1) : 75-91. doi: 10.3934/jmd.2014.8.75 |
[2] |
Michael Dellnitz, O. Junge, B Thiere. The numerical detection of connecting orbits. Discrete and Continuous Dynamical Systems - B, 2001, 1 (1) : 125-135. doi: 10.3934/dcdsb.2001.1.125 |
[3] |
Sabyasachi Karati, Palash Sarkar. Connecting Legendre with Kummer and Edwards. Advances in Mathematics of Communications, 2019, 13 (1) : 41-66. doi: 10.3934/amc.2019003 |
[4] |
Neal Koblitz, Alfred Menezes. Another look at security definitions. Advances in Mathematics of Communications, 2013, 7 (1) : 1-38. doi: 10.3934/amc.2013.7.1 |
[5] |
Isabelle Déchène. On the security of generalized Jacobian cryptosystems. Advances in Mathematics of Communications, 2007, 1 (4) : 413-426. doi: 10.3934/amc.2007.1.413 |
[6] |
Lan Wen. A uniform $C^1$ connecting lemma. Discrete and Continuous Dynamical Systems, 2002, 8 (1) : 257-265. doi: 10.3934/dcds.2002.8.257 |
[7] |
Vito Mandorino. Connecting orbits for families of Tonelli Hamiltonians. Journal of Modern Dynamics, 2012, 6 (4) : 499-538. doi: 10.3934/jmd.2012.6.499 |
[8] |
Alex Eskin, Maryam Mirzakhani. Counting closed geodesics in moduli space. Journal of Modern Dynamics, 2011, 5 (1) : 71-105. doi: 10.3934/jmd.2011.5.71 |
[9] |
Margarida Camarinha, Fátima Silva Leite, Peter Crouch. Riemannian cubics close to geodesics at the boundaries. Journal of Geometric Mechanics, 2022 doi: 10.3934/jgm.2022003 |
[10] |
Marek Fila, Hiroshi Matano. Connecting equilibria by blow-up solutions. Discrete and Continuous Dynamical Systems, 2000, 6 (1) : 155-164. doi: 10.3934/dcds.2000.6.155 |
[11] |
Francesca Alessio, Piero Montecchiari, Andres Zuniga. Prescribed energy connecting orbits for gradient systems. Discrete and Continuous Dynamical Systems, 2019, 39 (8) : 4895-4928. doi: 10.3934/dcds.2019200 |
[12] |
Palash Sarkar, Subhadip Singha. Verifying solutions to LWE with implications for concrete security. Advances in Mathematics of Communications, 2021, 15 (2) : 257-266. doi: 10.3934/amc.2020057 |
[13] |
Roberto Civino, Riccardo Longo. Formal security proof for a scheme on a topological network. Advances in Mathematics of Communications, 2021 doi: 10.3934/amc.2021009 |
[14] |
Riccardo Aragona, Alessio Meneghetti. Type-preserving matrices and security of block ciphers. Advances in Mathematics of Communications, 2019, 13 (2) : 235-251. doi: 10.3934/amc.2019016 |
[15] |
Archana Prashanth Joshi, Meng Han, Yan Wang. A survey on security and privacy issues of blockchain technology. Mathematical Foundations of Computing, 2018, 1 (2) : 121-147. doi: 10.3934/mfc.2018007 |
[16] |
Philip Lafrance, Alfred Menezes. On the security of the WOTS-PRF signature scheme. Advances in Mathematics of Communications, 2019, 13 (1) : 185-193. doi: 10.3934/amc.2019012 |
[17] |
Alexander Nabutovsky and Regina Rotman. Lengths of geodesics between two points on a Riemannian manifold. Electronic Research Announcements, 2007, 13: 13-20. |
[18] |
Samir Chowdhury, Facundo Mémoli. Explicit geodesics in Gromov-Hausdorff space. Electronic Research Announcements, 2018, 25: 48-59. doi: 10.3934/era.2018.25.006 |
[19] |
R. Bartolo, Anna Maria Candela, J.L. Flores. Timelike Geodesics in stationary Lorentzian manifolds with unbounded coefficients. Conference Publications, 2005, 2005 (Special) : 70-76. doi: 10.3934/proc.2005.2005.70 |
[20] |
Abbas Bahri. Attaching maps in the standard geodesics problem on $S^2$. Discrete and Continuous Dynamical Systems, 2011, 30 (2) : 379-426. doi: 10.3934/dcds.2011.30.379 |
2021 Impact Factor: 1.588
Tools
Metrics
Other articles
by authors
[Back to Top]