Page 1

Displaying 1 – 18 of 18

Showing per page

Semiconjugacy to a map of a constant slope

Jozef Bobok (2012)

Studia Mathematica

It is well known that any continuous piecewise monotone interval map f with positive topological entropy h t o p ( f ) is semiconjugate to some piecewise affine map with constant slope e h t o p ( f ) . We prove this result for a class of Markov countably piecewise monotone continuous interval maps.

Semidefinite characterisation of invariant measures for one-dimensional discrete dynamical systems

Didier Henrion (2012)

Kybernetika

Using recent results on measure theory and algebraic geometry, we show how semidefinite programming can be used to construct invariant measures of one-dimensional discrete dynamical systems (iterated maps on a real interval). In particular we show that both discrete measures (corresponding to finite cycles) and continuous measures (corresponding to chaotic behavior) can be recovered using standard software.

Shadowing and expansivity in subspaces

Andrew D. Barwell, Chris Good, Piotr Oprocha (2012)

Fundamenta Mathematicae

We address various notions of shadowing and expansivity for continuous maps restricted to a proper subset of their domain. We prove new equivalences of shadowing and expansive properties, we demonstrate under what conditions certain expanding maps have shadowing, and generalize some known results in this area. We also investigate the impact of our theory on maps of the interval.

Sharkovskiĭ's theorem holds for some discontinuous functions

Piotr Szuca (2003)

Fundamenta Mathematicae

We show that the Sharkovskiĭ ordering of periods of a continuous real function is also valid for every function with connected G δ graph. In particular, it is valid for every DB₁ function and therefore for every derivative. As a tool we apply an Itinerary Lemma for functions with connected G δ graph.

Some almost sure results for unbounded functions of intermittent maps and their associated Markov chains

J. Dedecker, S. Gouëzel, F. Merlevède (2010)

Annales de l'I.H.P. Probabilités et statistiques

We consider a large class of piecewise expanding maps T of [0, 1] with a neutral fixed point, and their associated Markov chains Yi whose transition kernel is the Perron–Frobenius operator of T with respect to the absolutely continuous invariant probability measure. We give a large class of unbounded functions f for which the partial sums of f○Ti satisfy both a central limit theorem and a bounded law of the iterated logarithm. For the same class, we prove that the partial sums of f(Yi) satisfy a...

Statistical properties of unimodal maps

Artur Avila, Carlos Gustavo Moreira (2005)

Publications Mathématiques de l'IHÉS

We consider typical analytic unimodal maps which possess a chaotic attractor. Our main result is an explicit combinatorial formula for the exponents of periodic orbits. Since the exponents of periodic orbits form a complete set of smooth invariants, the smooth structure is completely determined by purely topological data (“typical rigidity”), which is quite unexpected in this setting. It implies in particular that the lamination structure of spaces of analytic unimodal maps (obtained by the partition...

Structure of inverse limit spaces of tent maps with finite critical orbit

Sonja Štimac (2006)

Fundamenta Mathematicae

Using methods of symbolic dynamics, we analyze the structure of composants of the inverse limit spaces of tent maps with finite critical orbit. We define certain symmetric arcs called bridges. They are building blocks of composants. Then we show that the folding patterns of bridges are characterized by bridge types and prove that there are finitely many bridge types.

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...

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.

Currently displaying 1 – 18 of 18

Page 1