Results 1 - 10 of 854

SRB measures for partially hyperbolic systems whose central direction is mostly expanding

by José F. Alves, Christian Bonatti, Marcelo Viana , 2000
"... We construct Sinai-Ruelle-Bowen (SRB) measures supported on partially hyperbolic sets of diffeomorphisms -- the tangent bundle splits into two invariant subbundles, one of which is uniformly contracting -- under the assumption that the complementary subbundle is non-uniformly expanding. If the r ..."
Abstract - Cited by 197 (44 self) - Add to MetaCart
We construct Sinai-Ruelle-Bowen (SRB) measures supported on partially hyperbolic sets of diffeomorphisms -- the tangent bundle splits into two invariant subbundles, one of which is uniformly contracting -- under the assumption that the complementary subbundle is non-uniformly expanding

A Focus+Context Technique Based on Hyperbolic Geometry for Visualizing Large Hierarchies

by John Lamping, Ramana Rao, Peter Pirolli - SIGCHI CONFERENCE ON HUMAN FACTORS IN COMPUTING SYSTEMS (CHI '95) , 1995
"... We present a new focus+context (fisheye) technique for visualizing and manipulating large hierarchies. Our technique assigns more display space to a portion of the hierarchy while still embedding it in the context of the entire hierarchy. The essence of this scheme is to lay out the hierarchy in a ..."
Abstract - Cited by 411 (1 self) - Add to MetaCart
uniform way on a hyperbolic plane and map this plane onto a circular display region. This supports a smooth blending between focus and context, as well as continuous redirection of the focus. We have developed effective procedures for manipulating the focus using pointer clicks as well as interactive

Symbolic dynamics for hyperbolic flows

by Rufus Bowen - Amer. J. Math , 1973
"... Let/, {t e R) be a differentiable flow on a compact manifold M. A compact in-variant set A containing no fixed points is called hyperbolic if the tangent bundle restricted to A can be written as the Whitney sum of three Zyj-invariant continuous subbundles TAM = E + Es + Eu, where Eis the one-dimensi ..."
Abstract - Cited by 118 (0 self) - Add to MetaCart
Let/, {t e R) be a differentiable flow on a compact manifold M. A compact in-variant set A containing no fixed points is called hyperbolic if the tangent bundle restricted to A can be written as the Whitney sum of three Zyj-invariant continuous subbundles TAM = E + Es + Eu, where Eis the one

Uniformly accurate schemes for hyperbolic systems with relaxations

by Russel E. Caflisch, Shi Jin, Giovanni Russo - SIAM J. Numer. Anal , 1997
"... Abstract. We develop high-resolution shock-capturing numerical schemes for hyperbolic systems with relaxation. In such systems the relaxation time may vary from order-1 to much less than unity. When the relaxation time is small, the relaxation term becomes very strong and highly stiff, and underreso ..."
Abstract - Cited by 75 (23 self) - Add to MetaCart
Abstract. We develop high-resolution shock-capturing numerical schemes for hyperbolic systems with relaxation. In such systems the relaxation time may vary from order-1 to much less than unity. When the relaxation time is small, the relaxation term becomes very strong and highly stiff

Classification of Kleinian groups

by Bernard Maskit , 1974
"... We present here a complete classification of those Kleinian groups which have an invariant region of discontinuity and which, in their action on hyperbolic 3-space, have a finite-sided fundamental polyhedron. This classification is complete in the same sense that finitely-generated Fuchsian groups o ..."
Abstract - Cited by 208 (5 self) - Add to MetaCart
We present here a complete classification of those Kleinian groups which have an invariant region of discontinuity and which, in their action on hyperbolic 3-space, have a finite-sided fundamental polyhedron. This classification is complete in the same sense that finitely-generated Fuchsian groups

Uniformly hyperbolic surfaces

by Mario Bonk, Re Eremenko - Indiana Univ. Math. J , 2000
"... We prove the equivalence of certain uniform hyperbolicity conditions for open simply connected surfaces with non-positively curved intrinsic metric. ..."
Abstract - Cited by 11 (3 self) - Add to MetaCart
We prove the equivalence of certain uniform hyperbolicity conditions for open simply connected surfaces with non-positively curved intrinsic metric.

Uniform hyperbolicity of the graphs of curves

by Tarik Aougab , 2012
"... Abstract. Let C(Sg,p) denote the curve complex of the closed ori-entable surface of genus g with p punctures. Masur-Minksy and sub-sequently Bowditch showed that C(Sg,p) is δ-hyperbolic for some δ = δ(g, p). In this paper, we show that there exists some δ> 0 independent of g, p such that the curv ..."
Abstract - Cited by 9 (2 self) - Add to MetaCart
such that the curve graph C1(Sg,p) is δ-hyperbolic. Furthermore, we use the main tool in the proof of this theorem to show uniform boundedness of two other quantities which a priori grow with g and p: the curve complex distance between two vertex cycles of the same train track, and the Lipschitz constants of the map

Uniform hyperbolicity of the curve graphs

by Brian H. Bowditch , 2012
"... Abstract. We show that there is a universal constant, k, such that the curve graph associated to any compact orientable surface is k-hyperbolic. Independent proofs of this have been given by Aougab, by Hensel, Przytycki and Webb, and by Clay, Rafi and Schleimer. 1. ..."
Abstract - Cited by 8 (0 self) - Add to MetaCart
Abstract. We show that there is a universal constant, k, such that the curve graph associated to any compact orientable surface is k-hyperbolic. Independent proofs of this have been given by Aougab, by Hensel, Przytycki and Webb, and by Clay, Rafi and Schleimer. 1.

On the uniform hyperbolicity of some nonuniformly hyperbolic systems

by José F. Alves, Vítor Araújo, Benoît Saussol - 2003, p1303–1309. YONGLUO CAO, STEFANO LUZZATTO, AND ISABEL RIOS
"... Abstract. We give sufficient conditions for the uniform hyperbolicity of certain nonuniformly hyperbolic dynamical systems. In particular, we show that local diffeomorphisms that are nonuniformly expanding on sets of total probability are necessarily uniformly expanding. We also present a version of ..."
Abstract - Cited by 19 (3 self) - Add to MetaCart
Abstract. We give sufficient conditions for the uniform hyperbolicity of certain nonuniformly hyperbolic dynamical systems. In particular, we show that local diffeomorphisms that are nonuniformly expanding on sets of total probability are necessarily uniformly expanding. We also present a version

Uniform embeddability of relatively hyperbolic groups

by Marius Dadarlat, Erik Guentner , 2005
"... Abstract. Let Γ be a finitely generated group which is hyperbolic relative to a finite family {H1,...,Hn} of subgroups. We prove that Γ is uniformly embeddable in a Hilbert space if and only if each subgroup Hi is uniformly embeddable in a Hilbert space. 1. ..."
Abstract - Cited by 22 (2 self) - Add to MetaCart
Abstract. Let Γ be a finitely generated group which is hyperbolic relative to a finite family {H1,...,Hn} of subgroups. We prove that Γ is uniformly embeddable in a Hilbert space if and only if each subgroup Hi is uniformly embeddable in a Hilbert space. 1.
Results 1 - 10 of 854