
Previous Article
Nonautonomous 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 602082730 
2.  IMPA, Estrada Dona Castorina 110, Rio de Janeiro 22460320, 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) : 7591. doi: 10.3934/jmd.2014.8.75 
[2] 
Michael Dellnitz, O. Junge, B Thiere. The numerical detection of connecting orbits. Discrete & Continuous Dynamical Systems  B, 2001, 1 (1) : 125135. 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) : 4166. doi: 10.3934/amc.2019003 
[4] 
Neal Koblitz, Alfred Menezes. Another look at security definitions. Advances in Mathematics of Communications, 2013, 7 (1) : 138. 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) : 413426. doi: 10.3934/amc.2007.1.413 
[6] 
Lan Wen. A uniform $C^1$ connecting lemma. Discrete & Continuous Dynamical Systems  A, 2002, 8 (1) : 257265. doi: 10.3934/dcds.2002.8.257 
[7] 
Vito Mandorino. Connecting orbits for families of Tonelli Hamiltonians. Journal of Modern Dynamics, 2012, 6 (4) : 499538. doi: 10.3934/jmd.2012.6.499 
[8] 
Marek Fila, Hiroshi Matano. Connecting equilibria by blowup solutions. Discrete & Continuous Dynamical Systems  A, 2000, 6 (1) : 155164. doi: 10.3934/dcds.2000.6.155 
[9] 
Francesca Alessio, Piero Montecchiari, Andres Zuniga. Prescribed energy connecting orbits for gradient systems. Discrete & Continuous Dynamical Systems  A, 2019, 39 (8) : 48954928. doi: 10.3934/dcds.2019200 
[10] 
Alex Eskin, Maryam Mirzakhani. Counting closed geodesics in moduli space. Journal of Modern Dynamics, 2011, 5 (1) : 71105. doi: 10.3934/jmd.2011.5.71 
[11] 
Archana Prashanth Joshi, Meng Han, Yan Wang. A survey on security and privacy issues of blockchain technology. Mathematical Foundations of Computing, 2018, 1 (2) : 121147. doi: 10.3934/mfc.2018007 
[12] 
Philip Lafrance, Alfred Menezes. On the security of the WOTSPRF signature scheme. Advances in Mathematics of Communications, 2019, 13 (1) : 185193. doi: 10.3934/amc.2019012 
[13] 
Riccardo Aragona, Alessio Meneghetti. Typepreserving matrices and security of block ciphers. Advances in Mathematics of Communications, 2019, 13 (2) : 235251. doi: 10.3934/amc.2019016 
[14] 
Alexander Nabutovsky and Regina Rotman. Lengths of geodesics between two points on a Riemannian manifold. Electronic Research Announcements, 2007, 13: 1320. 
[15] 
Samir Chowdhury, Facundo Mémoli. Explicit geodesics in GromovHausdorff space. Electronic Research Announcements, 2018, 25: 4859. doi: 10.3934/era.2018.25.006 
[16] 
R. Bartolo, Anna Maria Candela, J.L. Flores. Timelike Geodesics in stationary Lorentzian manifolds with unbounded coefficients. Conference Publications, 2005, 2005 (Special) : 7076. doi: 10.3934/proc.2005.2005.70 
[17] 
Abbas Bahri. Attaching maps in the standard geodesics problem on $S^2$. Discrete & Continuous Dynamical Systems  A, 2011, 30 (2) : 379426. doi: 10.3934/dcds.2011.30.379 
[18] 
S. MaierPaape, Ulrich Miller. Connecting continua and curves of equilibria of the CahnHilliard equation on the square. Discrete & Continuous Dynamical Systems  A, 2006, 15 (4) : 11371153. doi: 10.3934/dcds.2006.15.1137 
[19] 
Patrick Guidotti. A family of nonlinear diffusions connecting PeronaMalik to standard diffusion. Discrete & Continuous Dynamical Systems  S, 2012, 5 (3) : 581590. doi: 10.3934/dcdss.2012.5.581 
[20] 
Jian Mao, Qixiao Lin, Jingdong Bian. Application of learning algorithms in smart home IoT system security. Mathematical Foundations of Computing, 2018, 1 (1) : 6376. doi: 10.3934/mfc.2018004 
2018 Impact Factor: 1.143
Tools
Metrics
Other articles
by authors
[Back to Top]