Ebook: Bifurcations and Catastrophes: Geometry of Solutions to Nonlinear Problems

Based on a lecture course at the Ecole Polytechnique (Paris), this text gives a rigorous introduction to many of the key ideas in nonlinear analysis, dynamical systems and bifurcation theory including catastrophe theory. Wherever appropriate it emphasizes a geometrical or coordinate-free approach which allows a clear focus on the essential mathematical structures. Taking a unified view, it brings out features common to different branches of the subject while giving ample references for more advanced or technical developments.

---

Based on a lecture course at the Ecole Polytechnique (Paris), this text gives a rigorous introduction to many of the key ideas in nonlinear analysis, dynamical systems and bifurcation theory including catastrophe theory. Wherever appropriate it emphasizes a geometrical or coordinate-free approach which allows a clear focus on the essential mathematical structures. Taking a unified view, it brings out features common to different branches of the subject while giving ample references for more advanced or technical developments.

---

Based on a lecture course at the Ecole Polytechnique (Paris), this text gives a rigorous introduction to many of the key ideas in nonlinear analysis, dynamical systems and bifurcation theory including catastrophe theory. Wherever appropriate it emphasizes a geometrical or coordinate-free approach which allows a clear focus on the essential mathematical structures. Taking a unified view, it brings out features common to different branches of the subject while giving ample references for more advanced or technical developments.
Content:
Front Matter....Pages I-VIII
Introduction....Pages 1-11
Local Inversion....Pages 13-30
Submanifolds....Pages 31-61
Transversality Theorems....Pages 63-86
Classification of Differentiable Functions....Pages 87-113
Catastrophe Theory....Pages 115-145
Vector Fields....Pages 147-177
Linear Vector Fields....Pages 179-217
Singular Points of Vector Fields....Pages 219-247
Closed Orbits — Structural Stability....Pages 249-268
Bifurcations of Phase Portraits....Pages 269-292
Back Matter....Pages 293-303

---

Based on a lecture course at the Ecole Polytechnique (Paris), this text gives a rigorous introduction to many of the key ideas in nonlinear analysis, dynamical systems and bifurcation theory including catastrophe theory. Wherever appropriate it emphasizes a geometrical or coordinate-free approach which allows a clear focus on the essential mathematical structures. Taking a unified view, it brings out features common to different branches of the subject while giving ample references for more advanced or technical developments.
Content:
Front Matter....Pages I-VIII
Introduction....Pages 1-11
Local Inversion....Pages 13-30
Submanifolds....Pages 31-61
Transversality Theorems....Pages 63-86
Classification of Differentiable Functions....Pages 87-113
Catastrophe Theory....Pages 115-145
Vector Fields....Pages 147-177
Linear Vector Fields....Pages 179-217
Singular Points of Vector Fields....Pages 219-247
Closed Orbits — Structural Stability....Pages 249-268
Bifurcations of Phase Portraits....Pages 269-292
Back Matter....Pages 293-303
....