3,236 research outputs found
Monotone periodic orbits for torus homeomorphisms
Let f be a homeomorphism of the torus isotopic to the identity and suppose
that there exists a periodic orbit with a non-zero rotation vector (p/q,r/q),
then f has a topologically monotone periodic orbit with the same rotation
vector.Comment: 10 pages, 1 figur
Simple braids for surface homeomorphisms
Let S be a compact, oriented surface with negative Euler characteristic and
let f be a homeomorphism of S that is isotopic to the identity. If there exists
a periodic orbit with a non-zero rotation vector, then there exists a simple
braid with the same rotation vector.Comment: 12 pages, 2 figure
On 3-manifolds that support partially hyperbolic diffeomorphisms
Let M be a closed 3-manifold that supports a partially hyperbolic
diffeomorphism f. If is nilpotent, the induced action of f on
is partially hyperbolic. If is almost nilpotent or if
has subexponential growth, M is finitely covered by a circle bundle
over the torus. If is almost solvable, M is finitely covered by a
torus bundle over the circle. Furthermore, there exist infinitely many
hyperbolic 3-manifolds that do not support dynamically coherent partially
hyperbolic diffeomorphisms; this list includes the Weeks manifold.
If f is a strong partially hyperbolic diffeomorphism on a closed 3-manifold M
and if is nilpotent, then the lifts of the stable and unstable
foliations are quasi-isometric in the universal of M. It then follows that f is
dynamically coherent.
We also provide a sufficient condition for dynamical coherence in any
dimension. If f is center bunched and if the center-stable and center-unstable
distributions are Lipschitz, then the partially hyperbolic diffeomorphism f
must be dynamically coherent.Comment: 21 page
Actions of SL(n,Z) on homology spheres
Any continuous action of SL(n,Z), where n > 2, on a r-dimensional mod 2
homology sphere factors through a finite group action if r < n - 1. In
particular, any continuous action of SL(n+2,Z) on the n-dimensional sphere
factors through a finite group action.Comment: 11 page
Zero entropy subgroups of mapping class groups
Let be a compact surface with boundary. We are interested in the question
of how a group action on permutes a finite invariant set . More precisely, how the algebraic properties of the induced group of
permutations of a finite invariant set affects the dynamical properties of the
group. Our main result shows that in many circumstances if the induced
permutation group is not solvable then among the homeomorphisms in the group
there must be one with a pseudo-Anosov component. We formulate this in terms of
the mapping class group relative to the finite set and show the stronger result
that in many circumstances (e.g. if ) this mapping
class group is itself solvable if it has no elements with pseudo-Anosov
components
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