This rigorous undergraduate introduction to dynamical systems is an accessible guide for mathematics students advancing from calculus.Hinweis: Dieser Artikel kann nur an eine deutsche Lieferadresse ausgeliefert werden.
Geoffrey R. Goodson is Professor of Mathematics at Towson University, Maryland. He previously served on the faculty of the University of Witwatersrand and the University of Cape Town. His research interests include dynamical systems, ergodic theory, matrix theory, and operator theory. He has published more than thirty papers, and taught numerous classes on dynamical systems.
Inhaltsangabe
1. The orbits of one-dimensional maps 2. Bifurcations and the logistic family 3. Sharkovsky's theorem 4. Dynamics on metric spaces 5. Countability, sets of measure zero, and the Cantor set 6. Devaney's definition of chaos 7. Conjugacy of dynamical systems 8. Singer's theorem 9. Conjugacy, fundamental domains, and the tent family 10. Fractals 11. Newton's method for real quadratics and cubics 12. Coppel's theorem and a proof of Sharkovsky's theorem 13. Real linear transformations, the Hénon Map, and hyperbolic toral automorphisms 14. Elementary complex dynamics 15. Examples of substitutions 16. Fractals arising from substitutions 17. Compactness in metric spaces and an introduction to topological dynamics 18. Substitution dynamical systems 19. Sturmian sequences and irrational rotations 20. The multiple recurrence theorem of Furstenberg and Weiss Appendix A: theorems from calculus Appendix B: the Baire category theorem Appendix C: the complex numbers Appendix D: Weyl's equidistribution theorem.
1. The orbits of one-dimensional maps 2. Bifurcations and the logistic family 3. Sharkovsky's theorem 4. Dynamics on metric spaces 5. Countability, sets of measure zero, and the Cantor set 6. Devaney's definition of chaos 7. Conjugacy of dynamical systems 8. Singer's theorem 9. Conjugacy, fundamental domains, and the tent family 10. Fractals 11. Newton's method for real quadratics and cubics 12. Coppel's theorem and a proof of Sharkovsky's theorem 13. Real linear transformations, the Hénon Map, and hyperbolic toral automorphisms 14. Elementary complex dynamics 15. Examples of substitutions 16. Fractals arising from substitutions 17. Compactness in metric spaces and an introduction to topological dynamics 18. Substitution dynamical systems 19. Sturmian sequences and irrational rotations 20. The multiple recurrence theorem of Furstenberg and Weiss Appendix A: theorems from calculus Appendix B: the Baire category theorem Appendix C: the complex numbers Appendix D: Weyl's equidistribution theorem.
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