Lectures on Dynamical Systems, Structural Stability, and Their ApplicationsThe communication of knowledge on nonlinear dynamical systems, between the mathematicians working on the analytic approach and the scientists working mostly on the applications and numerical simulations has been less than ideal. This volume hopes to bridge the gap between books written on the subject by mathematicians and those written by scientists. The second objective of this volume is to draw attention to the need for cross-fertilization of knowledge between the physical and biological scientists. The third aim is to provide the reader with a personal guide on the study of global nonlinear dynamical systems. |
Contents
Preface | 1 |
Topics in Topology and Differential Geometry | 24 |
Chapter 3 | 111 |
Chaper 4 | 145 |
Stability Theory and Liapunovs Direct Method | 198 |
Introduction to the General Theory of | 241 |
Chapter Applications | 324 |
| 399 | |
| 443 | |
Other editions - View all
Lectures On Dynamical Systems, Structural Stability And Their Applications Kotik K Lee Limited preview - 1992 |
Common terms and phrases
asymptotically stable automorphisms B₁ B₂ Banach space behavior called chaos chaotic closed orbit compact concept conjugacy continuous coordinate Corollary critical point defined definition denoted diffeomorphism differentiable manifold differential equations differential operator dimension discuss dx/dt dynamical systems eigenvalues equilibrium equivalence relation example exists feedback fiber bundle finite fixed point Furthermore geometric global Hamiltonian homeomorphism Hopf bifurcation hyperbolic integral curve invariant isomorphism Let f Lett Liapunov function Lie algebra Lie group linear Lipschitz Lorenz map f Math mathematical motion N₂ Nonetheless nonlinear open sets open subset optical origin oscillations parameters pendulum periodic orbit perturbations Phys positive properties qualitative respect semiconductor lasers sequence Smale smooth manifold solutions stable manifold strange attractors structurally stable submanifold subspace theory topological equivalence topological space transversality uniformly unique unstable vector bundle vector field vector space X₁ zero