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Points périodiques d’applications birationnelles de ℙ 2

Charles Favre (1998)

Annales de l'institut Fourier

Nous donnons une condition suffisante pour l’existence de points périodiques pour une application birationnelle de ℂ ℙ 2 . Sous cette hypothèse, une estimation précise du nombre de points périodiques de période fixée est obtenue. Nous donnons une application de ce résultat à l’étude dynamique de ces applications, en calculant explicitement l’auto-intersection de leur courant invariant naturellement associé. Nos résultats reposent essentiellement sur le théorème de Bézout donnant le cardinal de l’intersection...

Porcupine-like horseshoes: Transitivity, Lyapunov spectrum, and phase transitions

Lorenzo J. Díaz, Katrin Gelfert (2012)

Fundamenta Mathematicae

We study a partially hyperbolic and topologically transitive local diffeomorphism F that is a skew-product over a horseshoe map. This system is derived from a homoclinic class and contains infinitely many hyperbolic periodic points of different indices and hence is not hyperbolic. The associated transitive invariant set Λ possesses a very rich fiber structure, it contains uncountably many trivial and uncountably many non-trivial fibers. Moreover, the spectrum of the central Lyapunov exponents of...

Pressure and recurrence

Véronique Maume-Deschamps, Bernard Schmitt, Mariusz Urbański, Anna Zdunik (2003)

Fundamenta Mathematicae

We deal with a subshift of finite type and an equilibrium state μ for a Hölder continuous function. Let αⁿ be the partition into cylinders of length n. We compute (in particular we show the existence of the limit) l i m n → ∞ n - 1 l o g ∑ j = 0 τ ₙ ( x ) μ ( α ⁿ ( T j ( x ) ) ) , where α ⁿ ( T j ( x ) ) is the element of the partition containing T j ( x ) and τₙ(x) is the return time of the trajectory of x to the cylinder αⁿ(x).

Projectively Anosov flows with differentiable (un)stable foliations

Takeo Noda (2000)

Annales de l'institut Fourier

We consider projectively Anosov flows with differentiable stable and unstable foliations. We characterize the flows on T 2 which can be extended on a neighbourhood of T 2 into a projectively Anosov flow so that T 2 is a compact leaf of the stable foliation. Furthermore, to realize this extension on an arbitrary closed 3-manifold, the topology of this manifold plays an essential role. Thus, we give the classification of projectively Anosov flows on T 3 . In this case, the only flows on T 2 which extend to T 3 ...

Pruning theory and Thurston's classification of surface homeomorphisms

André de Carvalho, Toby Hall (2001)

Journal of the European Mathematical Society

Two dynamical deformation theories are presented – one for surface homeomorphisms, called pruning, and another for graph endomorphisms, called kneading – both giving conditions under which all of the dynamics in an open set can be destroyed, while leaving the dynamics unchanged elsewhere. The theories are related to each other and to Thurston’s classification of surface homeomorphisms up to isotopy.

Pseudo orbit tracing property and fixed points

Masatoshi Oka (1996)

Annales Polonici Mathematici

If a continuous map f of a compact metric space has the pseudo orbit tracing property and is h-expansive then the set of all fixed points of f is totally disconnected.

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