scholarly journals A Generalized Lyapunov Feature for Dynamical Systems on Riemannian Manifolds

2015 ◽  
Author(s):  
Rushil Anirudh ◽  
Vinay Venkataraman ◽  
Pavan Turaga
Keyword(s):  
Dynamical Systems ◽  
Riemannian Manifolds

Invariant tensor fields of dynamical systems with pinched Lyapunov exponents and rigidity of geodesic flows

1989 ◽  
Vol 9 (3) ◽  
pp. 427-432 ◽  
Author(s):  
Renato Feres ◽  
Anatoly Katok
Keyword(s):  
Dynamical Systems ◽  
Lyapunov Exponents ◽  
Riemannian Manifolds ◽  
Negative Curvature ◽  
Geodesic Flows ◽  
Tensor Fields ◽  
Invariant Tensor ◽  
Affine Connections

AbstractWe consider in this note smooth dynamical systems equipped with smooth invariant affine connections and show that, under a pinching condition on the Lyapunov exponents, certain invariant tensor fields are parallel. We then apply this result to a problem of rigidity of geodesic flows for Riemannian manifolds with negative curvature.

scholarly journals Periodic Orbits and Subharmonics of Dynamical Systems on Non-Compact Riemannian Manifolds

1996 ◽  
Vol 130 (1) ◽  
pp. 142-161 ◽  
Author(s):  
Silvia Cingolani ◽  
Elvira Mirenghi ◽  
Maria Tucci
Keyword(s):  
Dynamical Systems ◽  
Periodic Orbits ◽  
Riemannian Manifolds

LYAPUNOV EXPONENTS ON METRIC SPACES

2017 ◽  
Vol 97 (1) ◽  
pp. 153-162 ◽  
Author(s):  
C. A. MORALES ◽  
P. THIEULLEN ◽  
H. VILLAVICENCIO
Keyword(s):  
Lyapunov Exponent ◽  
Dynamical Systems ◽  
Ergodic Theory ◽  
Riemannian Manifolds ◽  
Metric Spaces ◽  
Lipschitz Constant ◽  
Topological Conjugacy ◽  
Asymptotically Stable ◽  
Characteristic Exponents ◽  
Stable Points

We use the pointwise Lipschitz constant to define an upper Lyapunov exponent for maps on metric spaces different to that given by Kifer [‘Characteristic exponents of dynamical systems in metric spaces’, Ergodic Theory Dynam. Systems3(1) (1983), 119–127]. We prove that this exponent reduces to that of Bessa and Silva on Riemannian manifolds and is not larger than that of Kifer at stable points. We also prove that it is invariant along orbits in the case of (topological) diffeomorphisms and under topological conjugacy. Moreover, the periodic orbits where this exponent is negative are asymptotically stable. Finally, we estimate this exponent for certain hyperbolic homeomorphisms.

Sign in / Sign up

Export Citation Format

Share Document