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Pesin theory consists of the study of the theory of non-uniformly hyperbolic diffeomorphisms. The aim of this book is to provide the reader with a straightforward account of this theory, following the approaches of Katok and Newhouse. The notes are divided into two parts. The first develops the basic theory, starting with general ergodic theory and introducing Liapunov exponents. Part Two deals with the applications of Pesin theory and contains an account of the existence (and distribution) of periodic points. It closes with a look at stable manifolds, and gives some results on absolute continuity. These lecture notes provide a unique introduction to Pesin theory and its applications. The author assumes that the reader has only a good background of undergraduate analysis and nothing further, so making the book accessible to complete newcomers to the field.
Ergodic theory. --- Manifolds (Mathematics) --- Geometry, Differential --- Topology --- Ergodic transformations --- Continuous groups --- Mathematical physics --- Measure theory --- Transformations (Mathematics)
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The focus of this book is on open conformal dynamical systems corresponding to the escape of a point through an open Euclidean ball. The ultimate goal is to understand the asymptotic behavior of the escape rate as the radius of the ball tends to zero. In the case of hyperbolic conformal systems this has been addressed by various authors. The conformal maps considered in this book are far more general, and the analysis correspondingly more involved. The asymptotic existence of escape rates is proved and they are calculated in the context of (finite or infinite) countable alphabets, uniformly contracting conformal graph-directed Markov systems, and in particular, conformal countable alphabet iterated function systems. These results have direct applications to interval maps, meromorphic maps and rational functions. Towards this goal the authors develop, on a purely symbolic level, a theory of singular perturbations of Perron--Frobenius (transfer) operators associated with countable alphabet subshifts of finite type and Hölder continuous summable potentials. This leads to a fairly full account of the structure of the corresponding open dynamical systems and their associated surviving sets.
Mathematics. --- Dynamics. --- Ergodic theory. --- Functional analysis. --- Functions of complex variables. --- Measure theory. --- Operator theory. --- Dynamical Systems and Ergodic Theory. --- Functional Analysis. --- Functions of a Complex Variable. --- Operator Theory. --- Measure and Integration. --- Functional analysis --- Lebesgue measure --- Measurable sets --- Measure of a set --- Algebraic topology --- Integrals, Generalized --- Measure algebras --- Rings (Algebra) --- Complex variables --- Elliptic functions --- Functions of real variables --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- Ergodic transformations --- Continuous groups --- Mathematical physics --- Measure theory --- Transformations (Mathematics) --- Dynamical systems --- Kinetics --- Mathematics --- Mechanics, Analytic --- Force and energy --- Mechanics --- Physics --- Statics --- Math --- Science --- Differentiable dynamical systems. --- Differential dynamical systems --- Dynamical systems, Differentiable --- Dynamics, Differentiable --- Differential equations --- Global analysis (Mathematics) --- Topological dynamics --- Conformal geometry. --- Conformal mapping. --- Conformal representation of surfaces --- Mapping, Conformal --- Transformation, Conformal --- Geometric function theory --- Mappings (Mathematics) --- Surfaces, Representation of --- Circular geometry --- Geometry of inverse radii --- Inverse radii, Geometry of --- Inversion geometry --- Möbius geometry --- Geometry
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Essentially a self-contained text giving an introduction to topological dynamics and ergodic theory.
Topological dynamics. --- Ergodic theory. --- Ergodic transformations --- Continuous groups --- Mathematical physics --- Measure theory --- Transformations (Mathematics) --- Dynamics, Topological --- Differentiable dynamical systems
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The classical theory of dynamical systems has tended to concentrate on Z-actions or R-actions. However in recent years there has been considerable progress in the study of higher dimensional actions (i.e. Zd or Rd with d>1). This book represents the proceedings of the 1993-4 Warwick Symposium on Zd actions. It comprises a mixture of surveys and original articles that span many of the diverse facets of the subject, including important connections with statistical mechanics, number theory and algebra. Researchers in ergodic theory and related fields will find that this book is an invaluable resource.
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Teoria ergòdica --- Fractals --- Termodinàmica --- Termologia --- Dinàmica --- Física --- Mecànica --- Bombes de calor --- Dinàmica de gasos --- Entalpia --- Entropia --- Mecànica estadística --- Processos irreversibles --- Radiació del cos negre --- Segon principi de la termodinàmica --- Termodinàmica atmosfèrica --- Termodinàmica del desequilibri --- Termoelasticitat --- Termoquímica --- Transferència de massa --- Anàlisi tèrmica --- Calor --- Fred --- Màquines tèrmiques --- Motors tèrmics --- Teoria quàntica --- Teoria de la dimensió (Topologia) --- Física matemàtica --- Grups continus --- Teoria de la mesura --- Transformacions (Matemàtica) --- Entropia (Teoria de la informació) --- Probabilitats --- Ergodic theory. --- Ergodic transformations --- Continuous groups --- Mathematical physics --- Measure theory --- Transformations (Mathematics)
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This volume arose from a semester at CIRM-Luminy on "Thermodynamic Formalism: Applications to Probability, Geometry and Fractals" which brought together leading experts in the area to discuss topical problems and recent progress. It includes a number of surveys intended to make the field more accessible to younger mathematicians and scientists wishing to learn more about the area. Thermodynamic formalism has been a powerful tool in ergodic theory and dynamical system and its applications to other topics, particularly Riemannian geometry (especially in negative curvature), statistical properties of dynamical systems and fractal geometry. This work will be of value both to graduate students and more senior researchers interested in either learning about the main ideas and themes in thermodynamic formalism, and research themes which are at forefront of research in this area.
Differential geometry. Global analysis --- Mathematics --- Classical mechanics. Field theory --- differentiaal geometrie --- dynamica
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Poincaré series. --- Poincaré, Séries de. --- Développements asymptotiques. --- Asymptotic expansions --- Automorphic functions --- Fonctions automorphes.
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