This widely used graduate text introduces modern topics in dynamical systems. The author includes new material on complex dynamics leading to key revisions. Striking color photos illustrating both Julia and Mandelbrot sets are included. This book assumes no prior acquaintance with advanced mathematical topics.
This widely used graduate text introduces modern topics in dynamical systems. The author includes new material on complex dynamics leading to key revisions. Striking color photos illustrating both Julia and Mandelbrot sets are included. This book assumes no prior acquaintance with advanced mathematical topics.
Robert L. Devaney is currently Professor of Mathematics at Boston University. He received his PhD from the University of California at Berkeley in under the direction of Stephen Smale. He taught at Northwestern University and Tufts University before coming to Boston University in 1980. His main area of research is dynamical systems, primarily complex analytic dynamics, but also including more general ideas about chaotic dynamical systems. Lately, he has become intrigued with the incredibly rich topological aspects of dynamics, including such things as indecomposable continua, Sierpinski curves, and Cantor bouquets. He is also the author of A First Course in Chaotic Dynamical Systems, Second Edition, published by CRC Press.
Inhaltsangabe
I One Dimensional Dynamics 1.A Visual and Historical Tour 2.Examples of Dynamical Systems 3.Elementary Definitions 4.Hyperbolicity 5.An Example: The Logistic Family 6.Symbolic Dynamics 7.Topological Conjugacy 8.Chaos 9.Structural Stability 10.Sharkovsky's Theorem 11.The Schwarzian Derivative 12.Bifurcations 13.Another View of Period Three 14.Period-Doubling Route to Chaos 15.Homoclinic Points and Bifurcations 16.Maps of the Circle 17.Morse-Smale Diffeomorphisms II Complex Dynamics 18.Quadratic Maps Revisited 19.Normal Families and Exceptional Points 20.Periodic Points 21.Properties of the Julia Set 22.The Geometry of the Julia Sets 23.Neutral Periodic Points 24.The Mandelbrot Set 25.Rational Maps 26.The Exponential Family III Higher Dimensional Dynamics 27.Dynamics of Linear Maps 28.The Smale Horseshoe Map 29.Hyperbolic Toral Automorphisms 30.Attractors 31.The Stable and Unstable Manifold Theorem 32.Global Results and Hyperbolic Maps 33.The Hopf Bifurcation 34.The Herron Map Appendix: Mathematical Preliminaries
I One Dimensional Dynamics 1.A Visual and Historical Tour 2.Examples of Dynamical Systems 3.Elementary Definitions 4.Hyperbolicity 5.An Example: The Logistic Family 6.Symbolic Dynamics 7.Topological Conjugacy 8.Chaos 9.Structural Stability 10.Sharkovsky's Theorem 11.The Schwarzian Derivative 12.Bifurcations 13.Another View of Period Three 14.Period-Doubling Route to Chaos 15.Homoclinic Points and Bifurcations 16.Maps of the Circle 17.Morse-Smale Diffeomorphisms II Complex Dynamics 18.Quadratic Maps Revisited 19.Normal Families and Exceptional Points 20.Periodic Points 21.Properties of the Julia Set 22.The Geometry of the Julia Sets 23.Neutral Periodic Points 24.The Mandelbrot Set 25.Rational Maps 26.The Exponential Family III Higher Dimensional Dynamics 27.Dynamics of Linear Maps 28.The Smale Horseshoe Map 29.Hyperbolic Toral Automorphisms 30.Attractors 31.The Stable and Unstable Manifold Theorem 32.Global Results and Hyperbolic Maps 33.The Hopf Bifurcation 34.The Herron Map Appendix: Mathematical Preliminaries
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