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A criterion for the positivity of the Liapunov characteristic exponent

Published online by Cambridge University Press:  19 September 2008

Eric Cornelis  and
Maciej Wojtkowski
Eric Cornelis
Affiliation:
Department of Mathematics, Facultes Universitaires Notre Dame de la Paix, Rempart de la Vierge, 8, B-5000 Namur, Belgium;
Maciej Wojtkowski
Affiliation:
Department of Mathematics, University of Arizona, Tucson, AZ 84721, USA and University of Warsaw, Poland
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Abstract

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We formulate sufficient conditions under which, for a finite subset of SL (2, ℝ), the maximal Liapunov exponent is positive. These conditions are based on the notion of compatible hyperbolicity. We then give an analytical formulation of such a condition and we apply this criterion to prove mixing properties of a particular transformation of the two-dimensional torus.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 4 , Issue 4 , December 1984 , pp. 527 - 539
Copyright
Copyright © Cambridge University Press 1984

References

REFERENCES

[1]Cornelis, E.. Sur les propriátás ergodiques de quelques transformations lineaires par morceaux du tore. Master's thesis, F.N.D.P.Namur, 1982.Google Scholar
[2]Oseledec, V. I.. A multiplicative ergodic theorem. Lyapunov characteristic numbers for dynamical systems. Trans. Moscow Math. Soc. 19 (1968), 197–231.Google Scholar
[3]Pesin, Ya. B.. Characteristic Lyapunov exponents and smooth ergodic theory. Russian Math. Surveys 32–4 (1977), 55–114.CrossRefGoogle Scholar
[4]Wojtkowski, M.. A model problem with the coexistence of stochastic and integrable behaviour. Commun. Math. Phys. 80 (1981), 453–464.CrossRefGoogle Scholar
[5]Wojtkowski, M.. On the ergodic properties of piecewise linear perturbations of the twist map. Ergod. Th. & Dynam. Sys. 2 (1982), 525–542.CrossRefGoogle Scholar