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LYAPUNOV EXPONENTS ON METRIC SPACES

  • C. A. MORALES (a1), P. THIEULLEN (a2) and H. VILLAVICENCIO (a3)

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.

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The first author was partially supported by CNPq from Brazil, the third author was partially supported by FONDECYT from Peru (C.G. 217–2014); the work was also partially supported by MATHAMSUB 15 MATH05-ERGOPTIM, Ergodic Optimization of Lyapunov Exponents.

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[8] Kifer, Y., ‘Characteristic exponents of dynamical systems in metric spaces’, Ergodic Theory Dynam. Systems 3(1) (1983), 119127.
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LYAPUNOV EXPONENTS ON METRIC SPACES

  • C. A. MORALES (a1), P. THIEULLEN (a2) and H. VILLAVICENCIO (a3)

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