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A Smale space is a chaotic dynamical system with canonical coordinates of contracting and expanding directions. The basic sets for Smale's Axiom A systems are a key class of examples. We consider the ...
Existence of complete Lyapunov functions for semiflows on separable metric spaces
Lyapunov functions Semiflows Separable metric space
2011/9/23
Abstract: The aim of this short note is to show how to construct a complete Lyapunov function of a semiflow by using a complete Lyapunov function of its time-one map. As a byproduct we assure the exis...
Higher cohomology for Anosov actions on certain homogeneous spaces
Higher cohomology Anosov actions certain homogeneous spaces
2011/9/19
Abstract: We study the smooth untwisted cohomology with real coefficients for the action on [SL(2, R) \times \cdot \cdot \cdot \times SL(2, R)]/{\Gamma} by the subgroup of diagonal matrices, where {\G...
Pure discrete spectrum in substitution tiling spaces
Pure discrete spectrum Tiling space Substitution
2011/9/14
Abstract: We introduce a procedure for establishing pure discrete spectrum for substitution tiling systems of Pisot family type and illustrate with several examples.
Minimal hyperspace actions of homeomorphism groups of h-homogeneous spaces
Minimal hyperspace actions universal minimal space h-homogeneous homogeneous Boolean algebra maximal chains generalized Cantor sets
2011/8/29
Abstract: Let X be a h-homogeneous zero-dimensional compact Hausdorff space, i.e. X is a Stone dual of a homogeneous Boolean algebra. Using the dual Ramsey theorem and a detailed combinatorial analysi...