TITLE

A variational principle for topological pressure for certain non-compact sets

AUTHOR(S)
Thompson, Daniel
PUB. DATE
December 2009
SOURCE
Journal of the London Mathematical Society;Dec2009, Vol. 80 Issue 3, p585
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
ABSTRACT
Let (X, d) be a compact metric space, let f:X ↦ X be a continuous map with the specification property and let ϕ: X ↦ ℝ be a continuous function. We prove a variational principle for topological pressure (in the sense of Pesin and Pitskel) for non-compact sets of the form Analogous results were previously known for topological entropy. As an application, we prove multifractal analysis results for the entropy spectrum of a suspension flow over a continuous map with specification and the dimension spectrum of certain non-uniformly expanding interval maps.
ACCESSION #
47431978

 

Related Articles

  • TOPOLOGICAL ENTROPY AND DISTRIBUTIONAL CHAOS. Smítal, Jaroslav // Real Analysis Exchange;Jun2006 Conference, Vol. 32, p61 

    The article examines whether there are implications between positive topological entropy and distributional chaos versions DC2 or DC3. It cites the introduction of the notion of distributional chaos for continuous maps of the interval [9] in 1994. It states that the three versions of...

  • TRIANGULAR MAPS NON-DECREASING ON THE FIBERS. Kocan, Zdenek // Real Analysis Exchange;2004/2005, Vol. 30 Issue 2, p519 

    There is a list of about 50 properties which characterize continuous maps of the interval with zero topological entropy. Most of them were proved by A. N. Sharkovsky [cf., e.g., Sharkovsky et al., Dynamics of One-Dimensional Mappings, Kluwer 1997]. It is also well known that only a few of these...

  • Complexity for Extended Dynamical Systems. Bonanno, Claudio; Collet, Pierre // Communications in Mathematical Physics;Oct2007, Vol. 275 Issue 3, p721 

    We consider dynamical systems for which the spatial extension plays an important role. For these systems, the notions of attractor, ϵ-entropy and topological entropy per unit time and volume have been introduced previously. In this paper we use the notion of Kolmogorov complexity to...

  • Pointwise Variation Growth and Entropy of the Descartes Product of a Few of Interval Maps. Risong Li; Zengxiong Cheng // Pure Mathematics;Oct2011, Vol. 1 Issue 3, p184 

    In this paper, the definition of pointwise variation growth of interval maps was extended to continuous self-maps on k-dimensional space I1 x I2 x�x Ik, where Ii is a closed interval. Let fi : Ii & larr; Ii be a continuous map and the total variation Due to image rights restrictions,...

  • Families, filters and chaos. Oprocha, Piotr // Bulletin of the London Mathematical Society;Aug2010, Vol. 42 Issue 4, p713 

    In this paper, we use the definition of (ℱ1, ℱ2)-chaos introduced recently by Tan and Xiong together with the properties of residual relations as a tool in construction of various kinds of scrambled sets. In particular, we show that a continuous map acting on a compact metric space...

  • Distribution of Maps with Transversal Homoclinic Orbits in a Continuous Map Space. Qiuju Xing; Yuming Shi // Abstract & Applied Analysis;2011, Special section p1 

    This paper is concerned with distribution of maps with transversal homoclinic orbits in a continuousmap space, which consists of continuousmaps defined in a closed and bounded set of a Banach space. By the transversal homoclinic theorem, it is shown that the map space contains a dense set of...

  • Equivalent Extensions to Caristi-Kirk's Fixed Point Theorem, Ekeland's Variational Principle, and Takahashi's Minimization Theorem. Zili Wu // Fixed Point Theory & Applications;2010, Special section p1 

    No abstract available.

  • On the relation between topological entropy and entropy dimension. Saltykov, P. S. // Mathematical Notes;Jun2009, Vol. 86 Issue 1/2, p255 

    For the Lipschitz mapping of a metric compact set into itself, there is a classical upper bound on topological entropy, namely, the product of the entropy dimension of the compact set by the logarithm of the Lipschitz constant. The Ghys conjecture is that, by varying the metric, one can...

  • A Local Approach to Yager Entropy of Dynamical Systems. Rahimi, Mehdi; Assari, Amir; Ramezani, Fatemeh // International Journal of Fuzzy Systems;Feb2016, Vol. 18 Issue 1, p98 

    In this paper, we define a type of Yager entropy for continuous dynamical systems on compact metric spaces. The concept of k-ergodic decomposition is introduced and applied to represent the new concept in terms of the Yager entropy in the sense of Riečan.

Share

Read the Article

Courtesy of THE LIBRARY OF VIRGINIA

Sorry, but this item is not currently available from your library.

Try another library?
Sign out of this library

Other Topics