Ergodic Theory and Dynamical Systems

Publisher: Cambridge University Press (CUP)

Impact Factor Rankings

2016 Impact Factor Available summer 2017 0.778 0.713 0.865 0.702 0.795 0.822 0.781 0.645 0.691 0.73 0.484 0.657 0.785 0.902 0.644 0.378 0.386 0.441 0.377 0.42 0.364 0.396 0.454

Impact factor over time

Impact factor
.
Year

5-year impact 0.80 >10.0 0.16 0.01 1.03 Ergodic theory and dynamical systems (Online), Ergodic theory and dynamical systems 1469-4417 41949087 Document, Periodical, Internet resource Internet Resource, Computer File, Journal / Magazine / Newspaper

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green

Publications in this journal

• Article: On Multicorns and Unicorns II: Bifurcations in Spaces of Antiholomorphic Polynomials
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ABSTRACT: The multicorns are the connectedness loci of unicritical antiholomorphic polynomials $\bar{z}^{d}+c$ . We investigate the structure of boundaries of hyperbolic components: we prove that the structure of bifurcations from hyperbolic components of even period is as one would expect for maps that depend holomorphically on a complex parameter (for instance, as for the Mandelbrot set; in this setting, this is a non-obvious fact), while the bifurcation structure at hyperbolic components of odd period is very different. In particular, the boundaries of odd period hyperbolic components consist only of parabolic parameters, and there are bifurcations between hyperbolic components along entire arcs, but only of bifurcation ratio 2. We also count the number of hyperbolic components of any period of the multicorns. Since antiholomorphic polynomials depend only real-analytically on the parameters, most of the techniques used in this paper are quite different from the ones used to prove the corresponding results in a holomorphic setting.
No preview · Article · Nov 2015 · Ergodic Theory and Dynamical Systems
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Article: Weak mixing for locally compact quantum groups
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ABSTRACT: We generalize the notion of weakly mixing unitary representations to locally compact quantum groups, introducing suitable extensions of all standard characterizations of weak mixing to this setting and establishing their equivalence. These results are used to complement the noncommutative Jacobs-de Leeuw-Glicksberg splitting theorem of Runde and the author ["Ergodic theory for quantum semigroups", J. Lond. Math. Soc. (2) 89 (2014) 941-959]. A relation between mixing and weak mixing of state-preserving actions of discrete quantum groups and the properties of certain inclusions of von Neumann algebras, which is known for discrete groups, is demonstrated. As another application, Wang's criterion for property (T) is generalized to discrete quantum groups.
Preview · Article · Apr 2015 · Ergodic Theory and Dynamical Systems
• Article: Coding of substitution dynamical systems as shifts of finite type
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ABSTRACT: We develop a theory that allows us to code dynamical systems induced by primitive substitutions continuously as shift of finite type in many different ways. The well-known prefix-suffix coding turns out to correspond to one special case. We precisely analyse the basic properties of these codings (injectivity, coding of the periodic points, properties of the presentation graph, interaction with the shift map). A lot of examples illustrate the theory and show that, depending on the particular coding, several amazing effects may occur. The results give new insights in the theory of substitution dynamical systems and might serve as a powerful tool for further researches.
No preview · Article · Nov 2014 · Ergodic Theory and Dynamical Systems
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Article: Minimality, transitivity, mixing and topological entropy on spaces with a free interval
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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.
Preview · Article · Dec 2013 · Ergodic Theory and Dynamical Systems
• Article: Bounded density shifts
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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.
No preview · Article · Dec 2013 · Ergodic Theory and Dynamical Systems
• Article: A volume preserving flow with essential coexistence of zero and non-zero Lyapunov exponents
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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.
No preview · Article · Dec 2013 · Ergodic Theory and Dynamical Systems
• Article: Continuation and Bifurcation Associated to the Dynamical Spectral Sequence
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ABSTRACT: In this paper we consider a filtered chain complex C and its differential given by a connection matrix Delta which determines an associated spectral sequence (E-r , d(r)). We present an algorithm which sweeps the connection matrix in order to span the modules E-r in terms of bases of C and gives the differentials d(r). In this process a sequence of similar connection matrices and associated transition matrices are produced. This algebraic procedure can be viewed as a continuation, where the transition matrices give information about the bifurcation behavior. We introduce directed graphs, called flow and bifurcation schematics, that depict bifurcations that could occur if the sequence of connection matrices and transition matrices were realized in a continuation of a Morse decomposition, and we present a dynamic interpretation theorem that provides conditions on a parameterized family of flows under which such a continuation could occur.
No preview · Article · Dec 2013 · Ergodic Theory and Dynamical Systems
• Article: Lamination languages
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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.
No preview · Article · Dec 2013 · Ergodic Theory and Dynamical Systems