Résumé
In recent years, due primarily to the proliferation of
computers, dynamical systems has again returned to its
roots in applications. It is the aim of this book to
provide undergraduate and beginning graduate students in
mathematics or science and engineering with a modest
foundation of knowledge. Equations in dimensions one and
two constitute the majority of the text, and in particular
it is demonstrated that the basic notion of stability and
bifurcations of vector fields are easily explained for
scalar autonomous equations. Further, the authors
investigate the dynamics of planar autonomous equations
where new dynamical behavior, such as periodic and
homoclinic orbits appears.
Contents
Pt. I Dimension One
Ch. 1 Scalar Autonomous Equations
Ch. 2 Elementary Bifurcations
Ch. 3 Scalar Maps
Pt. II Dimension One and One Half
Ch. 4 Scalar Nonautonomous Equations
Ch. 5 Bifurcation of Periodic Equations
Ch. 6 On Tori and Circles
Pt. III Dimension Two
Ch. 7 Planar Autonomous Systems
Ch. 8 Linear Systems
Ch. 9 Near Equilibria
Ch. 10 In the Presence of a Zero Eigenvalue
Ch. 11 In the Presence of Purely Imaginary
Eigenvalues
Ch. 12 Periodic Orbits
Ch. 13 All Planar Things Considered
Ch. 14 Conservative and Gradient Systems
Ch. 15 Planar Maps
Pt. IV Higher Dimensions
Ch. 16 Dimension Two and One Half
Ch. 17 Dimension Three
Ch. 18 Dimension Four
Appendix
References
Index
Caractéristiques techniques
| PAPIER | |
| Éditeur(s) | Springer |
| Auteur(s) | J. Hale, H. Koçak |
| Parution | 01/09/1991 |
| Nb. de pages | 568 |
| Format | 16 x 24 |
| Couverture | Relié |
| Poids | 905g |
| Intérieur | Noir et Blanc |
| EAN13 | 9780387971414 |
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