منابع مشابه
Symbolic Dynamics for the Geodesic Flow on Hecke Surfaces
In this paper we discuss a coding and the associated symbolic dynamics for the geodesic flow on Hecke triangle surfaces. We construct an explicit cross section for which the first return map factors through a simple (explicit) map given in terms of the generating map of a particular continued fraction expansion closely related to the Hecke triangle groups. We also obtain explicit expressions fo...
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We present a strategy for a geometric construction of cross sections for the geodesic flow on locally symmetric orbifolds of rank one. We work it out in detail for Γ\H, where H is the upper half plane and Γ = PΓ0(p), p prime. Its associated discrete dynamical system naturally induces a symbolic dynamics on R. The transfer operator produced from this symbolic dynamics has a particularly simple s...
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0. Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Part I. Renewal theorems in symbolic dynamics . . . . . . . . . . . . 1. Background: Shifts, suspension flows, thermodynamic formalism . 2. 3. 4. 5. 6. 7. 1 5 5 Renewal measures and renewal theorems . . . . . . . . . . . . . . 7 A modification for finite sequences . . . . . . . . . . . . . . . . . 10 Equidistribution theo...
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We introduce index systems, a tool for studying isolated invariant sets of dynamical systems that are not necessarily hyperbolic. The mapping of the index systems mimics the expansion and contraction of hyperbolic maps on the tangent space, and they may be used like Markov partitions to generate symbolic dynamics. Every continuous dynamical system satisfying a weak form of expansiveness possess...
متن کاملSymbolic dynamics for Lozi maps
We study the family of the Lozi maps La,b : R2 → R2, La,b(x, y) = (1+y−a|x|, bx), and their strange attractors Λa,b. We introduce the set of kneading sequences for the Lozi map and prove that it determines the symbolic dynamics for that map. We also introduce two other equivalent approaches. 2010 Mathematics Subject Classification: 37B10, 37D45, 37E30, 54H20
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ژورنال
عنوان ژورنال: Acta Mathematica
سال: 1981
ISSN: 0001-5962
DOI: 10.1007/bf02392459