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Symmetries of Julia sets of polynomial skew products on C^2
Complex dynamics skew product Green function
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2012/4/18
We consider the symmetries of Julia sets of polynomial skew products on C^2, which are birationally conjugate to rotational products. Our main results give the classification of the polynomial skew pr...
Integrability of higher pentagram maps
Integrability of higher pentagram maps Dynamical Systems
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2012/4/23
We define higher pentagram maps on polygons in $P^d$ for any dimension $d$, which extend R.Schwartz's definition of the 2D pentagram map. We prove their integrability for both closed and twisted polyg...
Decay of correlations for maps with uniformly contracting fibers and logarithm law for singular hyperbolic attractors
partial hyperbolicity singular-hyperbolicity recurrence decay of correlations local dimension hitting times
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2012/4/23
We consider two dimensional maps preserving a foliation which is uniformly contracting and a one dimensional associated quotient map having exponential convergence to equilibrium (iterates of Lebesgue...
Special representations of nilpotent Lie groups and the associated Poisson representations of current groups
Current group canonical representation special representation
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2012/4/18
In this paper we describe the new model of the representations of the current groups with a semisimple Lie group of the rank one. In the earlier papers of 70-80-th (Araki, Gelfand-Graev-Vershik) had p...
Banach representations and affine compactifications of dynamical systems
affine compactification affine flow Asplund space enveloping semigroup non-sensitivity right topological semigroup
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2012/4/18
To every Banach space V we associate a compact right topological affine semigroup E(V). We show that a separable Banach space V is Asplund if and only if E(V) is metrizable, and it is Rosenthal (i.e. ...
Fundamental domain of invariant sets and applications
Fundamental domain partial hyperbolicity cocycle transitivity accessibility essential saturation
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2012/4/18
Let $X$ be a compact metric space and $f:X\to X$ a homeomorphism on $X$. We construct a fundamental domain for the set with finite peaks for each cocycle induced by $\phi\in C(X,R)$. In particular we ...
Contracting Quadratic Operators of Bisexual Population
Quadratic stochastic operator fixed point trajectory contracting operators
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2012/4/18
In this paper we find a sufficient condition under which the operator of bisexual population is contraction and show that this condition is not necessary.
Entropy, Lyapunov exponents and the volume growth of boundary distortion under the action of dynamical systems
Lyapunov exponents the volume growth of boundary distortion the action of dynamical systems
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2012/4/17
We study the connection between the Lyapunov exponents and the volume growth of boundary distortion of regions in the phase space of the dynamical system.
Exponential growth of norms in semigroups of linear automorphisms and Hausdorff dimension of self-projective IFS
Exponential growth of norms semigroups of linear automorphisms Hausdorff dimension self-projective IFS Dynamical Systems
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2012/4/17
Given a finitely generated semigroup S of the (normed) set of linear maps of a vector space V into itself, we find sufficient conditions for the exponential growth of the number N(k) of elements of th...
More Universal Minimal Flows of Groups of Automorphisms of Uncountable Structures
Dynamical Systems
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2012/4/17
In this paper, we compute universal minimal flows of groups of automorphisms of uncountable $\omega$-homogeneous graphs, $K_n$-free graphs, hypergraphs, partially ordered sets, and their extensions wi...
Good measures on locally compact Cantor sets
Good measures locally compact Cantor sets Dynamical Systems
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2012/4/17
We study the set M(X) of full non-atomic Borel (finite or infinite) measures on a non-compact locally compact Cantor set X. For an infinite measure $\mu$ in M(X), the set $\mathfrak{M}_\mu = \{x \in X...
Minimum periods of homeomorphisms of orientable surfaces
Minimum periods homeomorphisms orientable surfaces Dynamical Systems
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2012/4/17
One of the main problems of the theory of dynamical systems is the determination of the existence of periodic orbits of a self-map and more generally, the structure of the set of periods. Define the m...
Postcritical sets and saddle basic sets for Axiom A polynomial skew products on C^2
Postcritical sets saddle basic sets Axiom A polynomial skew products C^2
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2012/2/29
Investigating the link between postcritical behaviors and the relations of saddle basic sets for Axiom A polynomial skew products on C^2, we characterize various properties concerning the three kinds ...
Skinning measures in negative curvature and equidistribution of equidistant submanifolds
Mixing equidistribution rate of mixing decay of correlation negative curvature
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2012/3/1
Let C be a locally convex subset of a negatively curved Riemannian manifold M. We define the skinning measure on the outer unit normal bundle to C in M by pulling back Patterson-Sullivan's measures at...