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Généralisation du théorème de Pesin pour l'α-entropie

Chapter 4: Deterministic Dynamical Systems

Part of the Lecture Notes in Mathematics book series (LNM,volume 1486)

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Soient M une variété compacte de dimension finie d, tε ]0,1[ et φ:M→M un T 1,t difféomorphisme préservant une mesure de Lebesgue m. Si hm(α,x,φ) désigne l'α-entropie de φ et μ1(x)≥μ2(x)≥...≥μd(x), les exposants de Lyapunov de l'application tangente Tφ, alors pour m-presque tout x:

$$\begin{gathered}h_m (\alpha ,x,\phi ) = \sum\limits_{i = 1}^d { [\mu _i (x) + \alpha ]^ + (\forall 0 \leqslant \alpha \leqslant - \mu _d (x)),} \hfill \\h_m (\alpha ,x,\phi ) = \alpha d (\forall \alpha \geqslant - \mu _d (x)). \hfill \\\end{gathered}$$

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Keywords

  • Lyapunov Exponent
  • Invariant Manifold
  • Springer Lecture Note
  • Characteristic Lyapunov Exponent
  • Multiplicative Ergodic Theorem

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© 1991 Springer-Verlag

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Thieullen, P. (1991). Généralisation du théorème de Pesin pour l'α-entropie. In: Arnold, L., Crauel, H., Eckmann, JP. (eds) Lyapunov Exponents. Lecture Notes in Mathematics, vol 1486. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0086673

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  • DOI: https://doi.org/10.1007/BFb0086673

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