Results 1  10
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40,329
Distortion results and invariant Cantor sets of unimodal maps, Ergodic Theory Dynam
 Systems
, 1994
"... Abstract. A distortion theory is developed for S−unimodal maps. It will be used to get some geometric understanding of invariant Cantor sets. In particular attracting Cantor sets turn out to have Lebesgue measure zero. Furthermore the ergodic behavior of S−unimodal maps is classified according to a ..."
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Cited by 35 (8 self)
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Abstract. A distortion theory is developed for S−unimodal maps. It will be used to get some geometric understanding of invariant Cantor sets. In particular attracting Cantor sets turn out to have Lebesgue measure zero. Furthermore the ergodic behavior of S−unimodal maps is classified according to a
Examples of groups that are measure equivalent to the free group. Ergodic Theory Dynam
 Systems
, 2005
"... Measure Equivalence (ME) is the measure theoretic counterpart of quasiisometry. This field grew considerably during the last years, developing tools to distinguish between different ME classes of countable groups. On the other hand, contructions of ME equivalent groups are very rare. We present a n ..."
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Cited by 28 (2 self)
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Measure Equivalence (ME) is the measure theoretic counterpart of quasiisometry. This field grew considerably during the last years, developing tools to distinguish between different ME classes of countable groups. On the other hand, contructions of ME equivalent groups are very rare. We present a new method, based on a notion of measurable freefactor, and we apply it to exhibit a new family of groups that are measure equivalent to the free group. We also present a quite extensive survey on results about Measure Equivalence for countable groups.
On the eigenvalues of finite rank BratteliVershik dynamical systems, Ergodic Theory Dynam
 Systems
"... Abstract. In this article we study conditions to be a continuous or a measurable eigenvalue of finite rank minimal Cantor systems, that is, systems given by an ordered Bratteli diagram with a bounded number of vertices per level. We prove that continuous eigenvalues always come from the stable subs ..."
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Cited by 8 (2 self)
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subspace associated to the incidence matrices of the Bratteli diagram and we study rationally independent generators of the additive group of continuous eigenvalues. Given an ergodic probability measure, we provide a general necessary condition to be a measurable eigenvalue. Then we consider two families
Groups of homeomorphisms of onemanifolds. III. Nilpotent subgroups, Ergodic Theory Dynam
 Systems
"... This selfcontained paper is part of a series [FF1, FF2] seeking to understand groups of homeomorphisms of manifolds in analogy with the theory of Lie groups and their discrete subgroups. PlanteThurston proved that every nilpotent subgroup of Diff 2 (S 1) is abelian. One of our main results is a sh ..."
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Cited by 25 (3 self)
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This selfcontained paper is part of a series [FF1, FF2] seeking to understand groups of homeomorphisms of manifolds in analogy with the theory of Lie groups and their discrete subgroups. PlanteThurston proved that every nilpotent subgroup of Diff 2 (S 1) is abelian. One of our main results is a
On almost automorphic dynamics in symbolic lattices, Ergodic Theory Dynam
 Systems
"... Abstract. We study the existence, structure, and topological entropy of almost automorphic arrays in symbolic lattice dynamical systems. In particular we show that almost automorphic arrays with arbitrarily large entropy are typical in symbolic lattice dynamical systems. Applications to pattern for ..."
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Cited by 4 (2 self)
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Abstract. We study the existence, structure, and topological entropy of almost automorphic arrays in symbolic lattice dynamical systems. In particular we show that almost automorphic arrays with arbitrarily large entropy are typical in symbolic lattice dynamical systems. Applications to pattern
The classification of nonsingular actions revisited, Ergodic Theory Dynam
 Systems
"... A simpler treatment is given of the theorems of Dye and Krieger concerning the classification of nonsingular ergodic transformations up to orbit equivalence. ..."
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Cited by 16 (0 self)
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A simpler treatment is given of the theorems of Dye and Krieger concerning the classification of nonsingular ergodic transformations up to orbit equivalence.
Dynamics of twodimensional Blaschke products. Ergodic Theory Dynam
 Systems
"... Abstract. In this paper we study the dynamics on T2 and C2 of a two dimensional Blaschke product. We prove that in the case that the Blaschke product is a diffeomorphism of T2 with all periodic points hyperbolic then the dynamics is hyperbolic. If a two dimensional Blaschke product diffeomorphism of ..."
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Cited by 1 (1 self)
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Abstract. In this paper we study the dynamics on T2 and C2 of a two dimensional Blaschke product. We prove that in the case that the Blaschke product is a diffeomorphism of T2 with all periodic points hyperbolic then the dynamics is hyperbolic. If a two dimensional Blaschke product diffeomorphism
Bounded hyperbolic components of quadratic rational maps. Ergodic Theory Dynam
 Systems
"... Let H be a hyperbolic component of quadratic rational maps possessing two distinct attracting cycles. We show that H has compact closure in moduli space if and only if neither attractor is a fixed point. ..."
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Cited by 17 (2 self)
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Let H be a hyperbolic component of quadratic rational maps possessing two distinct attracting cycles. We show that H has compact closure in moduli space if and only if neither attractor is a fixed point.
Spatial and nonspatial actions of Polish groups. Ergodic Theory Dynam
 Systems
"... Abstract. For locally compact groups all actions on a standard measure algebra have a spatial realization. For many Polish groups this is no longer the case. However, we show here that for nonarchimedean Polish groups all measure algebra actions do have spatial realizations. In the other direction ..."
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Cited by 12 (0 self)
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direction we show that an action of a Polish group is whirly (“ergodic at the identity”) if and only if it admits no spatial factors, and that all actions of a Lévy group are whirly. We also show that in the Polish group Aut (X,X, µ), for the generic automorphism T the action of the subgroup Λ(T) = cls
Results 1  10
of
40,329