Introduction to Dynamical Systems

Introduction 1. Examples and basic concepts 2. Topological dynamics 3. Symbolic dynamics 4. Ergodic theory 5. Hyperbolic dynamics 6. Ergodicity of Anosov diffeomorphisms 7. Low-dimensional dynamics 8. Complex dynamics 9. Measure-theoretic entropy Bibliography Index.

[1]  R. Devaney.  An Introduction to Chaotic Dynamical Systems , 1990 .

[2]  R. Robinson,et al.  Structural stability of C1 diffeomorphisms , 1976 .

[3]  Jonathan L. King,et al.  A map with topological minimal self-joinings in the sense of del Junco , 1990, Ergodic Theory and Dynamical Systems.

[4]  D. V. Anosov.  Tangent fields of transversal foliations in “U-systems” , 1967 .

[5]  J. Robbin.  A structural stability theorem , 1971 .

[6]  Paul R. Halmos,et al.  In General a Measure Preserving Transformation is Mixing , 1944 .

[7]  H. Furstenberg.  Ergodic behavior of diagonal measures and a theorem of Szemerédi on arithmetic progressions , 1977 .

[8]  R. F. Williams.  Lorenz knots are prime , 1984, Ergodic Theory and Dynamical Systems.

[9]  Sebastian van Strien.  New Directions in Dynamical Systems: Smooth Dynamics on the Interval (with an emphasis on quadratic-like maps) , 1988 .

[10]  Mitsuhiro Shishikura,et al.  On the quasiconformal surgery of rational functions , 1987 .

[11]  Douglas Lind,et al.  An Introduction to Symbolic Dynamics and Coding , 1995 .

[12]  Sergey Brin,et al.  The Anatomy of a Large-Scale Hypertextual Web Search Engine , 1998, Comput. Networks.

[13]  J. Hale,et al.  Methods of Bifurcation Theory , 1996 .

[14]  J. Eckmann,et al.  Iterated maps on the interval as dynamical systems , 1980 .

[15]  R L Graham,et al.  Ramsey's Theorem for a Class of Categories. , 1972, Proceedings of the National Academy of Sciences of the United States of America.

[16]  Y. Pesin.  CHARACTERISTIC LYAPUNOV EXPONENTS AND SMOOTH ERGODIC THEORY , 1977 .

[17]  Budapest,et al.  ON DIFFERENCE SETS OF SEQUENCES OF INTEGERS , 2002 .

[18]  Ricardo Mañé,et al.  A proof of the C1 stability conjecture , 1987 .

[19]  V. Bergelson,et al.  Ergodic Ramsey Theory–an Update , 1996 .

[20]  Fred W. Roush,et al.  THE WILLIAMS CONJECTURE IS FALSE FOR IRREDUCIBLE SUBSHIFTS , 1999 .

[21]  M. Feigenbaum.  The universal metric properties of nonlinear transformations , 1979 .

[22]  R. Adler,et al.  Entropy, a complete metric invariant for automorphisms of the torus. , 1967, Proceedings of the National Academy of Sciences of the United States of America.

[23]  Calvin C. Moore,et al.  ERGODICITY OF FLOWS ON HOMOGENEOUS SPACES. , 1966 .

[24]  H. Furstenberg,et al.  The Structure of Distal Flows , 1963 .

[25]  Benjamin Weiss,et al.  Topological dynamics and combinatorial number theory , 1978 .

[26]  P. Montel,et al.  Lecons sur les familles normales de fonctions analytiques et leurs applications , 1974 .

[27]  A. N. Sharkovskiĭ.  COEXISTENCE OF CYCLES OF A CONTINUOUS MAP OF THE LINE INTO ITSELF , 1995 .

[28]  I. Good,et al.  Ergodic theory and information , 1966 .

[29]  J. Milnor.  Topology from the differentiable viewpoint , 1965 .

[30]  Alan F. Beardon,et al.  Iteration of Rational Functions , 1991 .

[31]  E. Wright,et al.  An Introduction to the Theory of Numbers , 1939 .

[32]  W. Thurston,et al.  On iterated maps of the interval , 1988 .

[33]  R. F. Williams.  Classification of subshifts of finite type , 1973 .

[34]  E. T..  An Introduction to the Theory of Numbers , 1946, Nature.

[35]  Leopold Flatto,et al.  Geodesic flows, interval maps, and symbolic dynamics , 1991 .

[36]  David G. Sullivan,et al.  Solution of the Fatou - Julia problem on wandering domains , 1985 .

[37]  J. Mather,et al.  Characterization of Anosov Diffeomorphisms , 1968 .

[38]  J. Palis,et al.  Geometric theory of dynamical systems , 1982 .

[39]  J. H. van Lint,et al.  Functions of one complex variable II , 1997 .

[40]  Mike Boyle,et al.  Symbolic Dynamics and Matrices , 1993 .

[41]  R. Bowen,et al.  MARKOV PARTITIONS FOR AXIOM A DIFFEOMORPHISMS. , 1970 .

[42]  N. Friedman,et al.  Introduction to Ergodic Theory , 1971 .

[43]  E. Dinaburg.  ON THE RELATIONS AMONG VARIOUS ENTROPY CHARACTERISTICS OF DYNAMICAL SYSTEMS , 1971 .

[44]  F. R. Gantmakher.  The Theory of Matrices , 1984 .

[45]  L. Ahlfors.  Conformal Invariants: Topics in Geometric Function Theory , 1973 .

[46]  E. T. Bell.  Review: G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers , 1939 .

[47]  B. Weiss.  Subshifts of finite type and sofic systems , 1973 .

[48]  J. Yorke,et al.  Period Three Implies Chaos , 1975 .

[49]  G. Folland.  A course in abstract harmonic analysis , 1995 .

[50]  E. Szemeri~di,et al.  On Sets of Integers Containing No Four Elements in Arithmetic Progression , .

[51]  A. Douady,et al.  Systèmes dynamiques holomorphes , 1983 .

[52]  L. Wayne Goodwyn,et al.  Topological entropy bounds measure-theoretic entropy , 1969 .

[53]  Oscar E. LanfordIII.  A shorter proof of the existence of the Feigenbaum fixed point , 1984 .

[54]  P. Halmos.  Lectures on ergodic theory , 1956 .

[55]  A. Katok,et al.  Introduction to the Modern Theory of Dynamical Systems: INTRODUCTION , 1995 .

[56]  Y. Sinai,et al.  SOME SMOOTH ERGODIC SYSTEMS , 1967 .

[57]  Grzegorz W. KoŁodko,et al.  © Gordon and Breach, Science Publishers, Inc. , 1990 .

[58]  András Sárközy,et al.  On difference sets of sequences of integers. I , 1978 .

[59]  V. Rokhlin.  LECTURES ON THE ENTROPY THEORY OF MEASURE-PRESERVING TRANSFORMATIONS , 1967 .