Displaying similar documents to “Inhomogeneities in non-hyperbolic one-dimensional invariant sets”

Normal points for generic hyperbolic maps

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.

On the Hausdorff dimension of piecewise hyperbolic attractors

Tomas Persson (2010)

Fundamenta Mathematicae

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We study non-invertible piecewise hyperbolic maps in the plane. The Hausdorff dimension of the attractor is calculated in terms of the Lyapunov exponents, provided that the map satisfies a transversality condition. Explicit examples of maps for which this condition holds are given.

Boundaries of right-angled hyperbolic buildings

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.

Hyperbolic homeomorphisms and bishadowing

P. E. Kloeden, J. Ombach (1997)

Annales Polonici Mathematici

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Hyperbolic homeomorphisms on compact manifolds are shown to have both inverse shadowing and bishadowing properties with respect to a class of δ-methods which are represented by continuous mappings from the manifold into the space of bi-infinite sequences in the manifold with the product topology. Topologically stable homeomorphisms and expanding mappings are also considered.

Hyperbolicity in a class of one-dimensional maps.

Gregory J. Davis (1990)

Publicacions Matemàtiques

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In this paper we provide a direct proof of hyperbolicity for a class of one-dimensional maps on the unit interval. The maps studied are degenerate forms of the standard quadratic map on the interval. These maps are important in understanding the Newhouse theory of infinitely many sinks due to homoclinic tangencies in two dimensions.