Rigidity of Cylinders without Conjugate Points

Convex Hamiltonians without Conjugate Points

Introduction.

Exponential Growth of Spaces without Conjugate Points

An n-dimensional polyhedral space is a length space M (with intrinsic metric) triangulated into n-simplexes with smooth Riemannian metrics. In the definitions below, we assume that the triangulation is fixed. The boundary of M is the union of the (n− 1)-simplexes of the triangulation that are adjacent to only one (n− 1)-simplex. As usual, a geodesic in M is a naturally parametrized locally shor...

Piecewise monotone maps without periodic points: Rigidity, measures and complexity.

Piecewise monotone maps without periodic points : Rigidity , measures and complexity

We consider piecewise monotone maps of the interval with zero entropy or no periodic points. First, we give a rigid model for these maps: the interval translations mappings, possibly with ips. It follows, e.g., that the complexity of a piecewise monotone map of the interval is at most polynomial if and only if this map has a nite number of periodic points up to monotone equivalence. Second, we ...

The fundamental group of compact manifolds without conjugate points

The fundamental group of compact manifolds without conjugate points.