Dimension product structure of hyperbolic sets.
Hasselblatt, Boris, Schmeling, Jorg (2004)
Electronic Research Announcements of the American Mathematical Society [electronic only]
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Hasselblatt, Boris, Schmeling, Jorg (2004)
Electronic Research Announcements of the American Mathematical Society [electronic only]
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F. Przytycki, M. Urbański (1989)
Studia Mathematica
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Mark Pollicott (2009)
Fundamenta Mathematicae
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We consider families of hyperbolic maps and describe conditions for a fixed reference point to have its orbit evenly distributed for maps corresponding to generic parameter values.
Brian E. Raines (2004)
Fundamenta Mathematicae
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The topology of one-dimensional invariant sets (attractors) is of great interest. R. F. Williams [20] demonstrated that hyperbolic one-dimensional non-wandering sets can be represented as inverse limits of graphs with bonding maps that satisfy certain strong dynamical properties. These spaces have "homogeneous neighborhoods" in the sense that small open sets are homeomorphic to the product of a Cantor set and an arc. In this paper we examine inverse limits of graphs with more complicated...
Avalishvili, G., Gordeziani, D. (1999)
Bulletin of TICMI
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Michał Kisielewicz (1975)
Annales Polonici Mathematici
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Sudhanshu K. Ghoshal, Abha Ghoshal, M. Abu-Masood (1977)
Annales Polonici Mathematici
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Jan Dymara, Damian Osajda (2007)
Fundamenta Mathematicae
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We prove that the boundary of a right-angled hyperbolic building is a universal Menger space. As a consequence, the 3-dimensional universal Menger space is the boundary of some Gromov-hyperbolic group.
R. Krasnodębski (1970)
Colloquium Mathematicae
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Gallavotti, Giovanni (1998)
Documenta Mathematica
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J. Kisyński (1970)
Colloquium Mathematicae
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Romanov, V. G. (2003)
Sibirskij Matematicheskij Zhurnal
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Feliks Przytycki (2006)
Bulletin of the Polish Academy of Sciences. Mathematics
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e prove that the hyperbolic Hausdorff dimension of Fr Ω, the boundary of the simply connected immediate basin of attraction Ω to an attracting periodic point of a rational mapping of the Riemann sphere, which is not a finite Blaschke product in some holomorphic coordinates, or a 2:1 factor of a Blaschke product, is larger than 1. We prove a "local version" of this theorem, for a boundary repelling to the side of the domain. The results extend an analogous fact for...
Barreira, Luis, Pesin, Yakov, Schmeling, Jörg (1996)
Electronic Research Announcements of the American Mathematical Society [electronic only]
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Sergei Buyalo, Viktor Schroeder (2015)
Analysis and Geometry in Metric Spaces
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We characterize the boundary at infinity of a complex hyperbolic space as a compact Ptolemy space that satisfies four incidence axioms.
Douglas Dunham (1999)
Visual Mathematics
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Demirel, Oğuzhan, Soytürk, Emine (2008)
Novi Sad Journal of Mathematics
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Jacob Palis, Jean-Christophe Yoccoz (2009)
Publications Mathématiques de l'IHÉS
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In the present paper, we advance considerably the current knowledge on the topic of bifurcations of heteroclinic cycles for smooth, meaning C ∞, parametrized families {g t ∣t∈ℝ} of surface diffeomorphisms. We assume that a quadratic tangency q is formed at t=0 between the stable and unstable lines of two periodic points, not belonging to the same orbit, of a (uniformly hyperbolic) horseshoe K (see an example at the Introduction) and that such lines cross each other with positive relative...
Magnus Aspenberg (2009)
Fundamenta Mathematicae
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We show that Misiurewicz maps for which the Julia set is not the whole sphere are Lebesgue density points of hyperbolic maps.