世界图书出版公司出版图书现代动力系统理论导论 _生活百科

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现代动力系统理论导论(世界图书出版公司出版图书)【世界图书出版公司出版图书现代动力系统理论导论】《现代动力系统理论导论》是2011年4月1日世界图书出版公司出版的图书，作者是卡托克。本书主要讲述了现代动力系统的理论知识以及许多案例分析。
基本介绍书名：现代动力系统理论导论
作者：卡托克(Katok A.)
原版名称：Introduction to the modern theory of dynamical systems
ISBN：751003292X, 9787510032929
页数：802页
出版社：世界图书出版公司;
出版时间：2011年4月1日
开本：16开
作者简介编者：(美国)卡托克 (Katok A.)内容简介《现代动力系统理论导论(影印版)》内容简介：this book provides the first self-contained comprehensive exposition of the theory of dynamical systems as a core mathematical discipline closely intertwined with most of the main areas of mathematics. the authors introduce and rigorously develop the theory while providing researchers interested in applications with fundamental tools and paradigms.the book begins with a discussion of several elementary but fundamental examples. these are used to formulate a program for the general study of asymptotic properties and to introduce the principal theoretical concepts and methods. the main theme of the second part of the book is the interplay between local analysis near individual orbits and the global complexity of the orbit structure. the third and fourth parts develop in depth the theories of !ow-dimensional dynamical systems and hyperbolic dynamical systems.the book is aimed at students and researchers in mathematics at all levels from ad-vanced undergraduate up. scientists and engineers working in applied dynamics, non-linear science, and chaos will also find many fresh insights in this concrete and clear presentation. it contains more than four hundred systematic exercises.目录preface0. introduction1. principal branches of dynamics2. flows, vector fields, differential equations3. time-one map, section, suspension4. linearization and localizationpart 1examples and fundamental concepts1. firstexamples1. maps with stable asymptotic behaviorcontracting maps; stability of contractions; increasing interval maps2. linear maps3. rotations of the circle4. translations on the torus5. linear flow on the torus and completely integrable systems6. gradient flows7. expanding maps8. hyperbolic toral automorphisms9. symbolic dynamical systemssequence spaces; the shift transformation; topological markov chains; the perron-frobenius operator for positive matrices2. equivalence, classification, andinvariants1. smooth conjugacy and moduli for maps equivalence and moduli; local analytic linearization; various types of moduli2. smooth conjugacy and time change for flows3. topological conjugacy, factors, and structural stability4. topological classification of expanding maps on a circle expanding maps; conjugacy via coding; the fixed-point method5. coding, horseshoes, and markov partitionsmarkov partitions; quadratic maps; horseshoes; coding of the toral automor- phism6. stability of hyperbolic total automorphisms7. the fast-converging iteration method (newton method) for theconjugacy problem methods for finding conjugacies; construction of the iteration process8. the poincare-siegel theorem9. cocycles and cohomological equations3. principalclassesofasymptotictopologicalinvariants1. growth of orbitsperiodic orbits and the-function; topological entropy; volume growth; topo-logical complexity: growth in the fundamental group; homological growth2. examples of calculation of topological entropyisometries; gradient flows; expanding maps; shifts and topological markov chains; the hyperbolic toral automorphism; finiteness of entropy of lipschitz maps; expansive maps3. recurrence properties4.statistical behavior of orbits and introduction to ergodic theory1. asymptotic distribution and statistical behavior of orbitsasymptotic distribution, invariant measures; existence of invariant measures;the birkhoff ergodic theorem; existence of symptotic distribution; ergod-icity and unique ergodicity; statistical behavior and recurrence; measure-theoretic somorphism and factors2. examples of ergodicity; mixingrotations; extensions of rotations; expanding maps; mixing; hyperbolic total automorphisms; symbolic systems3. measure-theoretic entropyentropy and conditional entropy of partitions; entropy of a measure-preserving transformation; properties of entropy4. examples of calculation of measure-theoretic entropy rotations and translations; expanding maps; bernoulli and markov measures;hyperbolic total automorphisms5. the variational principle5.systems with smooth invar1ant measures and more examples1. existence of smooth invariant measuresthe smooth measure class; the perron-frobenius operator and divergence;criteria for existence of smooth invariant measures; absolutely continuous invariant measures for expanding maps; the moser theorem2. examples of newtonian systemsthe newton equation; free particle motion on the torus; the mathematical pendulum; central forces3. lagrangian mechanicsuniqueness in the configuration space; the lagrange equation; lagrangian systems; geodesic flows; the legendre transform4. examples of geodesic flowsmanifolds with many symmetries; the sphere and the toms; isometrics of the hyperbolic plane; geodesics of the hyperbolic plane; compact factors; the dynamics of the geodesic flow on compact hyperbolic surfaces5. hamiltonian systemssymplectic geometry; cotangent bundles; hamiltonian vector fields and flows;poisson brackets; integrable systems6. contact systemshamiltonian systems preserving a 1-form; contact forms7. algebraic dynamics: homogeneous and afline systemspart 2local analysis and orbit growth6.local hyperbolic theory and its applications 1. introduction2. stable and unstable manifoldshyperbolic periodic orbits; exponential splitting; the hadamard-perron the-orem; proof of the hadamard-perron theorem; the inclination lemma3. local stability of a hyperbolic periodic pointthe hartman-grobman theorem; local structural stability4. hyperbolic setsdefinition and invariant cones; stable and unstable manifolds; closing lemma and periodic orbits; locally maximal hyperbolic sets5. homoclinic points and horseshoesgeneral horseshoes; homoclinic points; horseshoes near homoclinic poi6. local smooth linearization and normal formsjets, formal power series, and smooth equivalence; general formal analysis; the hyperbolic smooth case7.transversality and genericity1. generic properties of dynamical systemsresidual sets and sets of first category; hyperbolicity and genericity2. genericity of systems with hyperbolic periodic pointstransverse fixed points; the kupka-smale theorem3. nontransversality and bifurcationsstructurally stable bifurcations; hopf bifurcations4. the theorem of artin and mazur8.orbitgrowtharisingfromtopology1. topological and fundamental-group entropies2. a survey of degree theorymotivation; the degree of circle maps; two definitions of degree for smooth maps; the topological definition of degree 3. degree and topological entropy4. index theory for an isolated fixed point5. the role of smoothness: the shub-sullivan theorem6. the lefschetz fixed-point formula and applications7. nielsen theory and periodic points for toral maps9.variational aspects of dynamics1. critical points of functions, morse theory, and dynamics2. the billiard problem3. twist mapsdefinition and examples; the generating function; extensions; birkhoff peri-odic orbits; global minimality of birkhoff periodic orbits4. variational description of lagrangian systems5. local theory and the exponential map6. minimal geodesics7. minimal geodesics on compact surfacespart 3low-dimensional phenomena10. introduction: what is low-dimensional dynamics?motivation; the intermediate value property and conformality; vet low-dimensional and low-dimensional systems; areas of !ow-dimensional dynamics11.homeomorphismsofthecircle1. rotation number2. the poincare classificationrational rotation number; irrational rotation number; orbit types and mea-surable classification12. circle diffeomorphisms1. the denjoy theorem2. the denjoy example3. local analytic conjugacies for diophantine rotation number4. invariant measures and regularity of conjugacies5. an example with singular conjugacy 6. fast-approximation methodsconjugacies of intermediate regularity; smooth cocycles with wild cobound-aries7. ergodicity with respect to lebesgue measure13. twist maps1. the regularity lemma2. existence of aubry-mather sets and homoclinic orbitsaubry-mather sets; invariant circles and regions of instability3. action functionals, minimal and ordered orbitsminimal action; minimal orbits; average action and minimal measures; stable sets for aubry-mather sets4. orbits homoclinic to aubry-mather sets5. nonexisience of invariant circles and localization of aubry-mather sets14.flowsonsurfacesandrelateddynamicalsystems1. poincare-bendixson theorythe poincare-bendixson theorem; existence of transversals2. fixed-point-free flows on the torusglobal transversals; area-preserving flows3. minimal sets4. new phenomenathe cherry flow; linear flow on the octagon5. interval exchange transformationsdefinitions and rigid intervals; coding; structure of orbit closures; invariant measures; minimal nonuniquely ergodic interval exchanges6. application to flows and billiardsclassification of orbits; parallel flows and billiards in polygons7. generalizations of rotation numberrotation vectors for flows on the torus; asymptotic cycles; fundamental class and smooth classification of area-preserving flows 15.continuousmapsoftheinterval1. markov covers and partitions2. entropy, periodic orbits, and horseshoes3. the sharkovsky theorem4. maps with zero topological entropy5. the kneading theory6. the tent model16.smoothmapsoftheinterval1. the structure of hyperbolic repellers2. hyperbolic sets for smooth maps3. continuity of entropy4. full families of unimodal mapspart 4hyperbolic dynamical systems17.surveyofexamples1. the smale attractor2. the da (derived from anosov) map and the plykin attractorthe da map; the plykln attractor3. expanding maps and anosov automorphisms of nilmanifolds4. definitions and basic properties of hyperbolic sets for flows5. geodesic flows on surfaces of constant negative curvature6. geodesic flows on compact riemannian manifolds with negative sectional curvature7. geodesic flows on rank-one symmetric spaces8. hyperbolic julia sets in the complex planerational maps of the riemann sphere; holomorphic dynamics18.topologicalpropertiesofhyperbolicsets1. shadowing of pseudo-orbits2. stability of hyperbolic sets and markov approximation3. spectral decomposition and specificationspectral decomposition for maps; spectral decomposition for flows; specifica- tion 4. local product structure5. density and growth of periodic orbits6. global classification of anosov diffeomorphisms on tori7. markov partitions19. metric structure of hyperbolic sets1. holder structuresthe invariant class of hsider-continuons functions; hslder continuity of conju-gacies; hslder continuity of orbit equivalence for flows; hslder continuity and differentiability of the unstable distribution; hslder continuity of the jacobian2. cohomological equations over hyperbolic dynamical systemsthe livschitz theorem; smooth invariant measures for anosov diffeomor-phisms; time change and orbit equivalence for hyperbolic flows; equivalence of torus extensions20.equilibriumstatesandsmoothinvariantmeasures1. bowen measure2. pressure and the variational principle3. uniqueness and classification of equilibrium statesuniqueness of equilibrium states; classification of equilibrium states4. smooth invariant measuresproperties of smooth invariant measures; smooth classification of anosov dif-feomorphisms on the torus; smooth classification of contact anosov flows on 3-manifolds5. margulis measure6. multiplicative asymptotic for growth of periodic pointslocal product flow boxes; the multiplicative asymptotic of orbit growth supplement s. dynamical systems with nonuniformly hyperbolic behavior byanatolekatokandleonardomendoza1. introduction2. lyapunov exponentscocycles over dynamical systems; examples of cocycles; the multiplicative ergodic theorem; osedelec-pesin e-reduction theorem; the rue!!e inequality3. regular neighborhoodsexistence of regular neighborhoods; hyperbolic points, admissible manifolds, and the graph transform4. hyperbolic measurespreliminaries; the closing lemma; the shadowing lemma; pseudo-markov covers; the livschitz theorem5. entropy and dynamics of hyperbolic measureshyperbolic measures and hyperbolic periodic points; continuous measures and transverse homoclinic points; the spectral decomposition theorem; entropy,horseshoes, and periodic points for hyperbolic measuresappendixa. background material1. basic topologytopological spaces; homotopy theory; metric spaces2. functional analysis3. differentiable manifoldsdifferentiable manifolds; tensor bundles; exterior calculus; transversality4. differential geometry5. topology and geometry of surfaces6. measure theorybasic notions; measure and topology7. homology theory8. locally compact groups and lie groupsnoteshintsandanswerstotheexercisesreferences index

世界图书出版公司出版图书 现代动力系统理论导论

世界图书出版公司出版图书现代动力系统理论导论