Page 1 Next

Displaying 1 – 20 of 23

Showing per page

Density of the set of symbolic dynamics with all ergodic measures supported on periodic orbits

Tatiane Cardoso Batista, Juliano dos Santos Gonschorowski, Fabio Armando Tal (2015)

Fundamenta Mathematicae

Let K be the Cantor set. We prove that arbitrarily close to a homeomorphism T: K → K there exists a homeomorphism T̃: K → K such that the ω-limit of every orbit is a periodic orbit. We also prove that arbitrarily close to an endomorphism T: K → K there exists an endomorphism T̃: K → K with every orbit finally periodic.

Equilibrium measures for holomorphic endomorphisms of complex projective spaces

Mariusz Urbański, Anna Zdunik (2013)

Fundamenta Mathematicae

Let f: ℙ → ℙ be a holomorphic endomorphism of a complex projective space k , k ≥ 1, and let J be the Julia set of f (the topological support of the unique maximal entropy measure). Then there exists a positive number κ f > 0 such that if ϕ: J → ℝ is a Hölder continuous function with s u p ( ϕ ) - i n f ( ϕ ) < κ f , then ϕ admits a unique equilibrium state μ ϕ on J. This equilibrium state is equivalent to a fixed point of the normalized dual Perron-Frobenius operator. In addition, the dynamical system ( f , μ ϕ ) is K-mixing, whence ergodic. Proving...

Equilibrium states for interval maps: the potential - t log | D f |

Henk Bruin, Mike Todd (2009)

Annales scientifiques de l'École Normale Supérieure

Let f : I I be a C 2 multimodal interval map satisfying polynomial growth of the derivatives along critical orbits. We prove the existence and uniqueness of equilibrium states for the potential φ t : x - t log | D f ( x ) | for t close to 1 , and also that the pressure function t P ( φ t ) is analytic on an appropriate interval near t = 1 .

Groupes de Schottky et comptage

Jean-François Quint (2005)

Annales de l’institut Fourier

Soient X un espace symétrique de type non compact et Γ un groupe discret d’isométries de X du type de Schottky. Dans cet article, nous donnons des équivalents des fonctions orbitales de comptage pour l’action de Γ sur X .

High-order phase transitions in the quadratic family

Daniel Coronel, Juan Rivera-Letelier (2015)

Journal of the European Mathematical Society

We give the first example of a transitive quadratic map whose real and complex geometric pressure functions have a high-order phase transition. In fact, we show that this phase transition resembles a Kosterlitz-Thouless singularity: Near the critical parameter the geometric pressure function behaves as x exp ( x 2 ) near x = 0 , before becoming linear. This quadratic map has a non-recurrent critical point, so it is non-uniformly hyperbolic in a strong sense.

Linear actions of free groups

Mark Pollicott, Richard Sharp (2001)

Annales de l’institut Fourier

In this paper we study dynamical properties of linear actions by free groups via the induced action on projective space. This point of view allows us to introduce techniques from Thermodynamic Formalism. In particular, we obtain estimates on the growth of orbits and their limiting distribution on projective space.

Multifractal spectra of Birkhoff averages for a piecewise monotone interval map

Franz Hofbauer (2010)

Fundamenta Mathematicae

We study the entropy spectrum of Birkhoff averages and the dimension spectrum of Lyapunov exponents for piecewise monotone transformations on the interval. In general, these transformations do not have finite Markov partitions and do not satisfy the specification property. We characterize these multifractal spectra in terms of the Legendre transform of a suitably defined pressure function.

On the Hyperbolic Hausdorff Dimension of the Boundary of a Basin of Attraction for a Holomorphic Map and of Quasirepellers

Feliks Przytycki (2006)

Bulletin of the Polish Academy of Sciences. Mathematics

e prove that the hyperbolic Hausdorff dimension of Fr Ω, the boundary of the simply connected immediate basin of attraction Ω to an attracting periodic point of a rational mapping of the Riemann sphere, which is not a finite Blaschke product in some holomorphic coordinates, or a 2:1 factor of a Blaschke product, is larger than 1. We prove a "local version" of this theorem, for a boundary repelling to the side of the domain. The results extend an analogous fact for polynomials...

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 ( x ) μ ( α ( T j ( x ) ) ) , where α ( 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).

Currently displaying 1 – 20 of 23

Page 1 Next