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This rigorous undergraduate introduction to dynamical systems is an accessible guide for mathematics students advancing from calculus.
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This rigorous undergraduate introduction to dynamical systems is an accessible guide for mathematics students advancing from calculus.
Produktdetails
- Produktdetails
- Verlag: Cambridge University Press
- Seitenzahl: 416
- Erscheinungstermin: 28. Dezember 2016
- Englisch
- Abmessung: 261mm x 182mm x 25mm
- Gewicht: 1058g
- ISBN-13: 9781107112674
- ISBN-10: 1107112672
- Artikelnr.: 46984695
- Verlag: Cambridge University Press
- Seitenzahl: 416
- Erscheinungstermin: 28. Dezember 2016
- Englisch
- Abmessung: 261mm x 182mm x 25mm
- Gewicht: 1058g
- ISBN-13: 9781107112674
- ISBN-10: 1107112672
- Artikelnr.: 46984695
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.
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.
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.
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.