LYAPUNOV EXPONENTS ON METRIC SPACES. Issue 1 (4th October 2017)

• Record Type: Journal Article
• Authors: MORALES, C. A.; THIEULLEN, P.; VILLAVICENCIO, H.
• Is Part Of: Bulletin of the Australian Mathematical Society. Volume 97:Issue 1(2018)
• Page Start: 153
• Page End: 162
• Publication Date: 2017-10-04
• Subjects: primary 54H20, -- secondary 58F15; upper Lyapunov exponent, -- metric space, -- pointwise Lipschitz constant; Mathematics -- Societies, etc; Mathematics -- Periodicals; 510.5
• DOI: 10.1017/S0004972717000703
• Languages: English
• ISSNs: 0004-9727

Abstract

Abstract : 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. Systems 3 (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.