Introduction to Dynamic Systems
Authors
Target audience
Higher education
Name: Introduction to Dynamic Systems
Author(s): Jacob Palis e Welington de Melo
Pages: 232
Publication: IMPA, 2017
ISBN: 978-85-244-0426-9
Edition: 2
1 Differentiable varieties and vector fields
0 Calculus in Rn and differentiable varieties
1 Vector fields on varieties
2 Topology in the space of applications C r
3 Tranversability
4 Structural stability
2 Local stability
1 Tubular flow theorem
2 Linear vector fields
3 Singularities and hyperbolic fixed points
4 Local stability
5 Local classification
6 Invariant varieties
7 The λ-lemma – geometric demonstration of local stability
3 The Kupka-Smale Theorem
1 Poincaré transformation
2 Genericity of vector fields
3 Transversality of invariant varieties
4 Genericity and stability of Morse-Smale fields
1 Morse-Smale fields – structural stability
2 Density of Morse-Smale fields on orientable surfaces
3 Generalizations
4 Difeomorphisms: general results on structural stability
The dynamics of monotone transformations of the circle
B Suggestions and selected problems
Bibliography
Rating Index
Index