Geodesic
Lyapunov exponents, KS-entropy and correlation decay in skew product extensions of Bernoulli endomorphisms
Bollettino della Unione matematica italiana, Série 8, 1B (1998) no. 3, pp. 631-638.

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Viene considerata una classe di sistemi dinamici del toro bidimensionale $T^{2}$ . Tali sistemi presentano la forma di un prodotto skew fra l'endomorfismo Bernoulli $B_{p}(x)=px \mod 1$, $p\in \mathbb{Z}\setminus \{-1,0,1\}$, definito sul toro undidimensionale $T^{1}\equiv [0, 1)$ ed una traslazione del toro stesso. Si dimostra che gli esponenti di Liapunov e l'entropia di Kolmogorov-Sinai della misura di Haar invariante possono essere calcolati esplicitamente. Viene infine discusso il decadimento delle correlazioni per i caratteri. 
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Siboni, S. Lyapunov exponents, KS-entropy and correlation decay in skew product extensions of Bernoulli endomorphisms. Bollettino della Unione matematica italiana, Série 8, 1B (1998) no. 3, pp. 631-638. http://geodesic.mathdoc.fr/item/BUMI_1998_8_1B_3_a7/

[1] L. M. Abramov - V. A. Rokhlin , The entropy of a skew product of measure-preserving transformations, Trans. Amer. Math. Soc. (Ser. 2), 48 (1965), 225-65. | Zbl

[2] A. Bazzani - S. Siboni - G. Turchetti - S. Vaienti , A model of modulated diffusion. Part I: analytical results, Jour. Stat. Phys., 76 (1994), 3/4, 929. | Zbl

[3] R. Bowen , Equilibrium States and the Ergodic Theory of Anosov Diffeomorphisms, Lecture Notes in Mathematics, 470 (1975). | MR | Zbl

[4] R. Mañé , Ergodic Theory and Differentiable Dynamics, Springer-Verlag, New York, N.Y. (1987). | MR | Zbl

[5] V. I. Oseledec , A multiplicative ergodic theorem, Trans. Moscow Math. Soc., 19 (1968), 197-231. | MR | Zbl

[6] W. Parry , Ergodic properties of a one-parameter family of skew-products, Nonlinearity, 8 (1995), 821-825. | MR | Zbl

[7] W. Parry - M. Pollicott , Zeta Functions and the Periodic Orbit Structure of Hyperbolic Dynamics, Ed. Astérisque. | MR | Zbl

[8] K. Petersen , Ergodic Theory, Cambridge University Press, Cambridge, 1983. | MR | Zbl

[9] M. S. Raghunathan , A proof of Oseledec's multiplicative ergodic theorem, Jsrael J. Math., 32 (1979), 356-362. | MR | Zbl

[10] D. Ruelle , An inequality for the entropy of differentiable maps, Bol. Soc. Bras. de Mat., 9 (1978), 83-87. | MR | Zbl

[11] D. Ruelle , Ergodic theory of differentiable dynamical systems, Publ. Math. IHES, 50 (1979), 275-306. | fulltext mini-dml | MR | Zbl

[12] S. Siboni , Analytical proof of the random phase approximation in a model of modulated diffusion, Jour. Phys. A, 25 (1994), 8171-8183. | MR | Zbl

[13] S. Siboni , Decay of correlations in skew endomorphisms with Bernoulli base, Bollettino Unione Matematica Italiana, 11-B (1997), 463-501. | MR | Zbl

[14] S. Siboni , Some ergodic properties of a mapping obtained by coupling the translation of the 1-torus with the endomorphism $2x \mod [0, 1)$, Nonlinearity, 7 (1994), 1133-1141. | MR | Zbl