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

ISBN-13: 9783540071846 / Angielski / Miękka / 1975 / 412 str.

A. Manning

Spis treści

1 Foliations with all leaves compact.- 2. A question concerning compact foliations.- 3. Compact leaves of foliations.- 4. Foliations with measure preserving holonomy.- 5. Foliated bundles, flat manifolds and invariant measures.- 6. A stable analytic foliation with only exceptional minimal sets.- 7. Accessibility and foliations.- 8. A Poincaré-Bendixson Theorem for R2-actions.- 9. Linearly induced vector fields and R2-actions on spheres.- 10. Structural stability for line fields with singularities on two-manifolds.- 11. Lie algebra preserving d iffeomorphisms.- 12. The point spectrum of the adjoint to an automorphism of a vector bundle.- 13. Structural stability for c1 diffeomorphisms.- 14. Absolute and infinitessimal stability.- 15. Classification of Anosov diffeomorphisms on Tori.- 16. Quasi-Anosov diffeomorphisms.- 17. Suspensions of topological Markov chains.- 18. Equilibrium states.- 19. Ergodic theory of Axiom A flows.- 20. Homology theory and dynamical systems.- 21. Topological entropy and stability.- 22. Cohomology of expanding attractors.- 23. Homology classes composed of infinitely many unstable manifolds of a dynamical system.- 24. Morse inequalities for diffeomorphisms with shoes and flows with solenoids.- 25. Arcs of Dynamical Systems : Bifurcations and Stability.- 26. Simple arcs and stable dynamical systems.- 27. Hilbert’s 16th problem : Limit cycles of polynomial vector fields in the plane.- 28. Topological conjugacy of real projective transformations.- 29. Fixed point index of area-preserving maps.- 30. Homoclinic points of area-preserving maps.- 31.Generic Bifurcations in Hamiltonian Systems.- 32. The Maslov index for Lagrangian manifolds.- 33. Contact equivalence for Lagrangian submanifolds.- 34. Optimisation of several functions.- 35. Bifurcation of Whitney Maps Rn ? R2 and Critical Pareto sets.- 36. A certain semilinear system of partial differential equations.- 37. Constrained Differential Equations.- 38. What is the Unit of Selection?.- 39. Zakalyukin’s proof of the (uni)versal unfolding theorem.- 40. The Catastrophe of a Buckling Beam.- 41. Reversals of the Earth’s Magnetic Field.- 42. Phase transitions as catastrophes.- 43.Caustics and catastrophes.- 44. Catastrophe theory in biology.- 45. Pyramidal Cells as Hierarchical Relators.- Solving a single conservation law.- Infinite codimension and transversality.- On infinitessimal and absolute stability of diffeomorphisms.- Expansive diffeomorphisms.- Stability of endomorphisms.- Topological entropy and the first homology group.- The implicit function theorem and analytic differential equations.- On simple arcs between structurally stable flows.- Nondifferentiability of invariant foliations.- Genericity theorems in topological dynamics.- The homology class of an expanded invariant manifold.- On the entropy conjecture.- Structural stability of C1 flows.- Removing index zero singularities with c1 small perturbations.- Sufficient conditions for an optimum.- Tolerance stability.- Geometric aspects of non-linear R.L.C. networks.- Regular stratifications.- Fifty problems in dynamical systems.- Dynamical systems : Five years after.- Catastrophe Theory : Its present state and future perspectives.- La théorie des catastrophes : état présent et perspectives.- Catastrophe Theory : A reply to Thom.- Answer to Christopher Zeeman’s reply.- Author Index.