491 research outputs found
Convergence to equilibrium for intermittent symplectic maps
We investigate a class of area preserving non-uniformly hyperbolic maps of
the two torus. First we establish some results on the regularity of the
invariant foliations, then we use this knowledge to estimate the rate of
mixing.Comment: LaTeX, 23 page
Universal models for Lorenz maps
The existence of smooth families of Lorenz maps exhibiting all possible
dynamical behavior is established and the structure of the parameter space of
these families is described
The Rigidity Conjecture
A central question in dynamics is whether the topology of a system determines
its geometry. This is known as rigidity. Under mild topological conditions
rigidity holds for many classical cases, including: Kleinian groups, circle
diffeomorphisms, unimodal interval maps, critical circle maps, and circle maps
with a break point. More recent developments show that under similar
topological conditions, rigidity does not hold for slightly more general
systems. In this paper we state a conjecture which describes how topological
classes are organized into rigidity classes.Comment: 6 page
Focal Rigidity of Flat Tori
Given a closed Riemannian manifold (M, g), there is a partition \Sigma_i of
its tangent bundle TM called the focal decomposition. The sets \Sigma_i are
closely associated to focusing of geodesics of (M, g), i.e. to the situation
where there are exactly i geodesic arcs of the same length joining points p and
q in M. In this note, we study the topological structure of the focal
decomposition of a closed Riemannian manifold and its relation with the metric
structure of the manifold. Our main result is that the flat n-tori are focally
rigid, in the sense that if two flat tori are focally equivalent, then the tori
are isometric up to rescaling.Comment: 10 page
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