5 papers
Periodic Points on the 2-sphere
Charles Pugh, Michael Shub
For a degree two latitude preserving endomorphism of the 2-sphere, we show that has periodic points.
Hölder foliations, revisited
Charles Pugh, Michael Shub, Amie Wilkinson
We investigate transverse Hölder regularity of some canonical leaf conjugacies in partially hyperbolic dynamical systems and transverse Hölder regularity of some invariant foliatio…
Jordan curves and funnel sections
Charles Pugh, Conan Wu
We study the case when solution of an ODE at a given initial condition fail to be unique and investigate what are the possible time-1 sections of the `solution funnel'. Along the w…
The Boundary between Compact and Noncompact Complete Riemann Manifolds
D. Holcman, C. Pugh
In 1941 Sumner Myers proved that if the Ricci curvature of a complete Riemann manifold has a positive infimum then the manifold is compact and its diameter is bounded in terms of t…
Partial differentiability of invariant splittings
Charles Pugh, Michael Shub, Amie Wilkinson
A key feature of a general nonlinear partially hyperbolic dynamical system is the absence of differentiability of its invariant splitting. In this paper, we show that often partial…