
Previous Article
Axiom a systems without sinks and sources on $n$manifolds
 DCDS Home
 This Issue

Next Article
Nonautonomous and random attractors for delay random semilinear equations without uniqueness
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] 
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 
[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] 
Lan Wen. A uniform $C^1$ connecting lemma. Discrete & Continuous Dynamical Systems  A, 2002, 8 (1) : 257265. doi: 10.3934/dcds.2002.8.257 
[6] 
Vito Mandorino. Connecting orbits for families of Tonelli Hamiltonians. Journal of Modern Dynamics, 2012, 6 (4) : 499538. doi: 10.3934/jmd.2012.6.499 
[7] 
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 
[8] 
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 
[9] 
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 
[10] 
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 
[11] 
Alexander Nabutovsky and Regina Rotman. Lengths of geodesics between two points on a Riemannian manifold. Electronic Research Announcements, 2007, 13: 1320. 
[12] 
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 
[13] 
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 
[14] 
Liqun Qi, Zheng yan, Hongxia Yin. Semismooth reformulation and Newton's method for the security region problem of power systems. Journal of Industrial & Management Optimization, 2008, 4 (1) : 143153. doi: 10.3934/jimo.2008.4.143 
[15] 
Artur O. Lopes, Rafael O. Ruggiero. Large deviations and AubryMather measures supported in nonhyperbolic closed geodesics. Discrete & Continuous Dynamical Systems  A, 2011, 29 (3) : 11551174. doi: 10.3934/dcds.2011.29.1155 
[16] 
Vladimir S. Matveev and Petar J. Topalov. Metric with ergodic geodesic flow is completely determined by unparameterized geodesics. Electronic Research Announcements, 2000, 6: 98104. 
[17] 
Alice Le Brigant. Computing distances and geodesics between manifoldvalued curves in the SRV framework. Journal of Geometric Mechanics, 2017, 9 (2) : 131156. doi: 10.3934/jgm.2017005 
[18] 
Tapio Rajala. Improved geodesics for the reduced curvaturedimension condition in branching metric spaces. Discrete & Continuous Dynamical Systems  A, 2013, 33 (7) : 30433056. doi: 10.3934/dcds.2013.33.3043 
[19] 
Jonathan Chaika, Yitwah Cheung, Howard Masur. Winning games for bounded geodesics in moduli spaces of quadratic differentials. Journal of Modern Dynamics, 2013, 7 (3) : 395427. doi: 10.3934/jmd.2013.7.395 
[20] 
Flavia Antonacci, Marco Degiovanni. On the Euler equation for minimal geodesics on Riemannian manifoldshaving discontinuous metrics. Discrete & Continuous Dynamical Systems  A, 2006, 15 (3) : 833842. doi: 10.3934/dcds.2006.15.833 
2016 Impact Factor: 1.099
Tools
Metrics
Other articles
by authors
[Back to Top]