Beyond Hyperbolicity: Expansion Properties of One Dimensional MappingsMathematical Sciences Institute, Cornell University, 1990 - 22 pages |
Common terms and phrases
absolutely continuous invariant absorbing Cantor sets Army Research Office attracting Cantor set bounded independent chain rule formula class of S-unimodal Conjugacies between unimodal constructed continuous invariant measure CORNELL UNIVERSITY LIBRARIES critical point critical value dark realm dependence to initial derivative along trajectories Desargues Theorem Mathematics diffeomorphisms DIMENSIONAL MAPPINGS dynamical systems existence of absolutely EXPANSION PROPERTIES exponential finite absolutely continuous finite union fixed point funnel geometric growth rate Hausdorff dimension homeomorphism HYPERBOLICITY indifferent period orbit infinitely renormalizable initial conditions intervals fi(J John Guckenheimer Library White Hall map ƒ map of ƒ Mathematical Sciences Institute metric structure number of iterates orbit of period parameter families parameter values giving periodic point positive Lyapunov exponent quasisymmetric reduce any growth renormalization of f satisfy Axiom Schwarzian derivative sensitive dependence set of parameter stable periodic orbits Stewart Johnson stopping rules structurally stable Tka+k topological attractors topological equivalence classes transformation ƒ transformations with absolutely U.S. Army Research unimodal transformations