Ergodic Theory and Dynamical Systems

Publisher: Cambridge University Press

Description

  • Impact factor
    0.87
  • 5-year impact
    1.02
  • Cited half-life
    0.00
  • Immediacy index
    0.14
  • Eigenfactor
    0.01
  • Article influence
    1.21
  • Other titles
    Ergodic theory and dynamical systems (Online), Ergodic theory and dynamical systems
  • ISSN
    1469-4417
  • OCLC
    41949087
  • Material type
    Document, Periodical, Internet resource
  • Document type
    Internet Resource, Computer File, Journal / Magazine / Newspaper

Publisher details

Cambridge University Press

  • Pre-print
    • Author can archive a pre-print version
  • Post-print
    • Author can archive a post-print version
  • Conditions
    • On authors personal or departmental web page or institutional repository or PubMed Central
    • Pre-print to record acceptance for publication
    • Publisher copyright and source must be acknowledged
    • Must link to publisher version
    • Authors version may be deposited immediately on acceptance
    • Publishers version/PDF may be used on authors personal or departmental web page any time after publication
    • Publishers version/PDF may be used in an institutional repository or PubMed Central after 12 month embargo
    • Articles in some journals can be made Open Access on payment of additional charge
    • If funding agency rules apply, authors may post articles in PubMed Central 12 months after publication or use Cambridge Open Option
    • Permission (not to be unreasonably withheld) needs to be sought if the author is at a different institution to when the article was originally published.
  • Classification
    ​ green

Publications in this journal

  • [Show abstract] [Hide abstract]
    ABSTRACT: In this paper some aspects on chaotic behavior and minimality in planar piecewise smooth vector fields theory are treated. The occurrence of non-deterministic chaos is observed and the concept of orientable minimality is introduced. It is also investigated some relations between minimality and orientable minimality and observed the existence of new kinds of non-trivial minimal sets in chaotic systems. The approach is geometrical and involve the ordinary techniques of non-smooth systems.
    Ergodic Theory and Dynamical Systems 04/2014;
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    ABSTRACT: We consider subshifts of the full shift of bi-infinite sequences with alphabet \$\{ 0, 1, \ldots , n- 1\} \$ defined by not allowing the sum of finite words to exceed a value depending on its length. These shifts we call bounded density shifts. We study these shifts in detail and make a comparison on the similarities to but also differences from the well-known \$\beta \$-shifts.
    Ergodic Theory and Dynamical Systems 12/2013; 33(06).
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    ABSTRACT: Leaves of laminations can be symbolically represented by deforming them into paths of labeled embedded carrier graphs, including train tracks. Here, we describe and characterize the languages of two-way infinite words coming from this kind of coding, called lamination languages, first, by using carrier graph sequences, and second, by using word combinatorics. These characterizations generalize those existing for interval exchange transformations. We also show that lamination languages have ultimately affine factor complexity, and we present effective techniques to build these languages.
    Ergodic Theory and Dynamical Systems 12/2013; 33(06).
  • Ergodic Theory and Dynamical Systems 12/2013;
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    ABSTRACT: We study dynamics of continuous maps on compact metrizable spaces containing a free interval (i.e. an open subset homeomorphic to an open interval). Special attention is paid to relationships between topological transitivity, weak and strong topological mixing, dense periodicity and topological entropy as well as to the topological structure of minimal sets. In particular, a trichotomy for minimal sets and a dichotomy for transitive maps are proved.
    Ergodic Theory and Dynamical Systems 12/2013; 33(06).
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    ABSTRACT: We demonstrate essential coexistence of hyperbolic and non-hyperbolic behavior in the continuous-time case by constructing a smooth volume preserving flow on a five-dimensional compact smooth manifold that has non-zero Lyapunov exponents almost everywhere on an open and dense subset of positive but not full volume and is ergodic on this subset while having zero Lyapunov exponents on its complement. The latter is a union of three-dimensional invariant submanifolds, and on each of these submanifolds the flow is linear with Diophantine frequency vector.
    Ergodic Theory and Dynamical Systems 12/2013; 33(06).
  • Ergodic Theory and Dynamical Systems 10/2013; 33(05).
  • Ergodic Theory and Dynamical Systems 10/2013; 33(05).
  • Ergodic Theory and Dynamical Systems 08/2013; 33(04).
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    ABSTRACT: This paper contains results on the geometric and ergodic properties of a class of strange attractors introduced by Wang and Young [Towards a theory of rank one attractors. Ann. of Math. (2) 167 (2008), 349–480]. These attractors can live in phase spaces of any dimension, and have been shown to arise naturally in differential equations that model several commonly occurring phenomena. Dynamically, such systems are chaotic; they have controlled non-uniform hyperbolicity with exactly one unstable direction, hence the name rank-one. In this paper we prove theorems on their Lyapunov exponents, Sinai–Ruelle–Bowen (SRB) measures, basins of attraction, and statistics of time series, including central limit theorems, exponential correlation decay and large deviations. We also present results on their global geometric and combinatorial structures, symbolic coding and periodic points. In short, we build a dynamical profile for this class of dynamical systems, proving that these systems exhibit many of the characteristics normally associated with ‘strange attractors’.
    Ergodic Theory and Dynamical Systems 08/2013; 33(04).
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    ABSTRACT: The Ruelle operator has been studied extensively both in dynamical systems and iterated function systems (IFSs). Given a weakly contractive IFS \$(X, \{w_j\}_{j=1}^m)\$ and an associated family of positive continuous potential functions \$\{p_j\}_{j=1}^m\$, a triple system \$(X, \{w_j\}_{j=1}^m, \{p_j\}_{j=1}^m)\$is set up. In this paper we study Ruelle operators associated with the triple systems. The paper presents an easily verified condition. Under this condition, the Ruelle operator theorem holds provided that the potential functions are Dini continuous. Under the same condition, the Ruelle operator is quasi-compact, and the iterations sequence of the Ruelle operator converges with a specific geometric rate, if the potential functions are Lipschitz continuous.
    Ergodic Theory and Dynamical Systems 08/2013; 33(04).
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    ABSTRACT: If a partially hyperbolic diffeomorphism on a torus of dimension \$d\geq 3\$ has stable and unstable foliations which are quasi-isometric on the universal cover, and its centre direction is one-dimensional, then the diffeomorphism is leaf conjugate to a linear toral automorphism. In other words, the hyperbolic structure of the diffeomorphism is exactly that of a linear, and thus simple to understand, example. In particular, every partially hyperbolic diffeomorphism on the 3-torus is leaf conjugate to a linear toral automorphism.
    Ergodic Theory and Dynamical Systems 06/2013; 33(03).
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    ABSTRACT: We give an almost self-contained group theoretic proof of Furstenberg’s structure theorem as generalized by Ellis: each minimal compact distal flow is the result of a transfinite sequence of equicontinuous extensions, and their limits, starting from a flow consisting of a singleton. The groups that we use are CHART groups, and their basic properties are recalled at the beginning of the paper.
    Ergodic Theory and Dynamical Systems 06/2013; 33(03).
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    ABSTRACT: Beyond the uncoupled regime, the rigorous description of the dynamics of (piecewise) expanding coupled map lattices remains largely incomplete. To address this issue, we study repellers of periodic chains of linearly coupled Lorenz-type maps which we analyze by means of symbolic dynamics. Whereas all symbolic codes are admissible for sufficiently small coupling intensity, when the interaction strength exceeds a chain length independent threshold, we prove that a large bunch of codes is pruned and an extensive decay follows suit for the topological entropy. This quantity, however, does not immediately drop off to 0. Instead, it is shown to be continuous at the threshold and to remain extensively bounded below by a positive number in a large part of the expanding regime. The analysis is firstly accomplished in a piecewise affine setting where all calculations are explicit and is then extended by continuation to coupled map lattices based on \$C^1\$-perturbations of the individual map.
    Ergodic Theory and Dynamical Systems 06/2013; 33(03).
  • [Show abstract] [Hide abstract]
    ABSTRACT: If (M,F) is a C 4 compact Finsler surface of genus at least two without conjugate points, we show that the first integrals of the geodesic flow are constant. Using this fact, we show that if (M,F) is also of Landsberg type then (M,F) is Riemannian. The connection between the absence of conjugate points and the Riemannian character of the Finsler metric has some remarkable consequences concerning rigidity.
    Ergodic Theory and Dynamical Systems 04/2013; 33(02).
  • [Show abstract] [Hide abstract]
    ABSTRACT: We give a complete characterization of the compact metric dynamical systems that appear as boundaries of the canonical compactification of a locally compact countable state mixing Markov shift. Consider such a compact metric dynamical system. Then there is a pair of non-conjugate Markov shifts with conjugate canonical compactifications, one of which has the given compact system as canonical boundary.
    Ergodic Theory and Dynamical Systems 04/2013; 33(02).
  • [Show abstract] [Hide abstract]
    ABSTRACT: Ultraproducts of measure preserving actions of countable groups are used to study the graph combinatorics associated with such actions, including chromatic, independence and matching numbers. Applications are also given to the theory of random colorings of Cayley graphs and sofic actions and equivalence relations.
    Ergodic Theory and Dynamical Systems 04/2013; 33(02).

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