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S-unimodal Misiurewicz maps with flat critical points

Roland Zweimüller (2004)

Fundamenta Mathematicae

We consider S-unimodal Misiurewicz maps T with a flat critical point c and show that they exhibit ergodic properties analogous to those of interval maps with indifferent fixed (or periodic) points. Specifically, there is a conservative ergodic absolutely continuous σ-finite invariant measure μ, exact up to finite rotations, and in the infinite measure case the system is pointwise dual ergodic with many uniform and Darling-Kac sets. Determining the order of return distributions to suitable reference...

Sur les homéomorphismes du cercle de classe P C r par morceaux ( r ≥ 1 ) qui sont conjugués C r par morceaux aux rotations irrationnelles

Abdelhamid Adouani, Habib Marzougui (2008)

Annales de l’institut Fourier

Soit r ≥ 1 un réel. Ici, on étudie les homéomorphismes du cercle qui sont de classe P C r par morceaux et de nombres de rotation irrationnels. On caractérise ceux qui sont C r par morceaux conjugués à des C r -difféomorphismes. Comme conséquence, on obtient un critère de conjugaison...

Symbolic dynamics and Lyapunov exponents for Lozi maps

Diogo Baptista, Ricardo Severino (2012)

ESAIM: Proceedings

Building on the kneading theory for Lozi maps introduced by Yutaka Ishii, in 1997, we introduce a symbolic method to compute its largest Lyapunov exponent. We use this method to study the behavior of the largest Lyapunov exponent for the set of points whose forward and backward orbits remain bounded, and find the maximum value that the largest Lyapunov exponent can assume.

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