Global Theory of Dynamical Systems

Z. Nitecki

• 01 augustus 1980
• 9783540102366

Samenvatting:

Morse-smale fields of geodesics.- Periodic points and topological entropy of one dimensional maps.- Ergodicity of linked twist maps.- Infinitesimal hyperbolicity implies hyperbolicity.- A qualitative singular perturbation theorem.- On a theorem of conley and smoller.- Positively expansive maps of compact manifolds.- An algorithm for finding closed orbits.- Linked twist mappings are almost anosov.- Symbolic dynamics, homology, and knots.- Anomalous anosov flows.- Efficiency vs. hyperbolicity on tori.- Dynamical behavior of geodesic fields.- The growth of topological entropy for one dimensional maps.- Separatrices, non-isolated invariant sets and the seifert conjecture.- Construction of invariant measures absolutely continuous with respect to dx for some maps of the interval.- The estimation from above for the topological entropy of a diffeomorphism.- Ergodicity in (G,?)-extensions.- A probabilistic version of bowen - Ruelle's volume lemma.- Periodically forced relaxation oscillations.- Moduli of stability for diffeomorphisms.- Uncountably many distinct topologically hyperbolic equilibria in ?4.- Dynamical properties of certain non-commutative skew-products.- A note on explosive flows.- Intertwining invariant manifolds and the lorenz attractor.- Counting compatible boundary conditions.- Stable manifolds for maps.- Singular points of planar vector fields.- Gradient vectorfields near degenerate singularities.- Invariant curves near parabolic points and regions of stability.- Motion under the influence of a strong constraining force.- Conjugacies of topologically hyperbolic fixed points: A necessary condition on foliations.- Coleman's conjecture on topological hyperbolicity.- Population dynamics from game theory.