Dynamical Systems—Warwick 1974: Proceedings of a Symposium Held at the University of Warwick 1973/74

David Epstein (auth.), Dr. Anthony Manning (eds.)9780387071848, 0-387-07184-9

Table of contents :
Foliations with all leaves compact….Pages 1-2
A question concerning compact foliations….Pages 2-4
Compact leaves of foliations….Pages 4-6
Foliations with measure preserving holonomy….Pages 6-7
Foliated bundles, flat manifolds and invariant measures….Pages 8-9
A stable analytic foliation with only exceptional minimal sets….Pages 9-10
Accessibility and foliations….Pages 10-12
A Poincaré-Bendixson Theorem for R 2 -actions….Pages 12-13
Linearly induced vector fields and R 2 -actions on spheres….Pages 13-17
Structural stability for line fields with singularities on two-manifolds….Pages 17-19
Lie algebra preserving diffeomorphisms….Pages 19-20
The point spectrum of the adjoint to an automorphism of a vector bundle….Pages 20-21
Structural stability for C 1 diffeomorphisms….Pages 21-23
Absolute and infinitessimal stability….Pages 24-26
Classification of Anosov diffeomorphisms on Tori….Pages 26-27
Quasi-Anosov diffeomorphisms….Pages 27-29
Suspensions of topological Markov chains….Pages 30-31
Equilibrium states….Pages 32-35
Ergodic theory of Axiom A flows….Pages 35-36
Homology theory and dynamical systems….Pages 36-39
Topological entropy and stability….Pages 39-40
Cohomology of expanding attractors….Pages 41-42
Homology classes composed of infinitely many unstable manifolds of a dynamical system….Pages 42-44
Morse inequalities for diffeomorphisms with shoes and flows with solenoids….Pages 44-47
Arcs of Dynamical Systems: Bifurcations and Stability….Pages 48-53
Simple arcs and stable dynamical systems….Pages 53-55
Hilbert’s 16th problem: Limit cycles of polynomial vector fields in the plane….Pages 55-57
Topological conjugacy of real projective transformations….Pages 57-59
Fixed point index of area-preserving maps….Pages 59-60
Homoclinic points of area preserving maps….Pages 60-61
Generic Bifurcations in Hamiltonian Systems….Pages 62-70
The Maslov index for Lagrangian manifolds….Pages 70-71
Contact equivalence for Lagrangian submanifolds….Pages 71-73
Optimisation of several functions….Pages 73-75
Bifurcation of Whitney Maps ℝ n →ℝ 2 and Critical Pareto sets….Pages 75-77
A certain semilinear system of partial differential equations….Pages 78-79
Constrained Differential Equations….Pages 80-82
What is the Unit of Selection?….Pages 82-84
Zakalyukin’s proof of the (uni)versal unfolding theorem….Pages 85-86
The Catastrophe of a Buckling Beam….Pages 86-91
Reversals of the Earth’s Magnetic Field….Pages 91-98
Phase transitions as catastrophes….Pages 98-100
Caustics and catastrophes….Pages 100-101
Catastrophe theory in biology….Pages 101-105
Pyramidal Cells as Hierarchical Relators….Pages 105-107
Solving a single conservation law….Pages 108-134
Infinite codimension and transversality….Pages 135-150
On infinitessimal and absolute stability of diffeomorphisms….Pages 151-161
Expansive diffeomorphisms….Pages 162-174
Stability of endomorphisms….Pages 175-184
Topological Entropy and the First Homology Group….Pages 185-190
The implicit function theorem and analytic differential equations….Pages 191-208
On simple arcs between structurally stable flows….Pages 209-233
Nondifferentiability of invariant foliations….Pages 234-240
Genericity theorems in topological dynamics….Pages 241-250
The homology class of an expanded invariant manifold….Pages 251-256
On the entropy conjecture: a report on conversations among R. Bowen M. Hirsch, A. Manning, C. Pugh, B. Sanderson, M. Shub and R. Williams….Pages 257-261
Structural stability of C 1 flows….Pages 262-275
Removing index-zero singularities with C 1 -small perturbations….Pages 278-286
Sufficient conditions for an optimum….Pages 287-292
Tolerance Stability….Pages 293-304
Geometric Aspects of Non-linear R.L.C. Networks….Pages 305-331
Regular stratifications….Pages 332-344
Fifty problems in dynamical systems….Pages 345-353
Dynamical systems—five years after….Pages 354-365
Catastrophe Theory: Its present state and future perspectives….Pages 366-366
La Théorie des Catastrophes: Etat Présent et Perspectives….Pages 366-372
Catastrophe Theory: A reply to thom….Pages 373-383
Answerto Christopher Zeeman’s reply….Pages 384-389