451 research outputs found
On period minimal pseudo-Anosov braids
A family of period minimal pseudo-Anosov braids, one for each pair of Farey neighbors in [0, 1/2], is described
New Rotation Sets in a Family of Torus Homeomorphisms
We construct a family of homeomorphisms of the
two-torus isotopic to the identity, for which all of the rotation sets
can be described explicitly. We analyze the bifurcations and
typical behavior of rotation sets in the family, providing insight into the
general questions of toral rotation set bifurcations and prevalence. We show
that there is a full measure subset of , consisting of infinitely many
mutually disjoint non-trivial closed intervals, on each of which the rotation
set mode locks to a constant polygon with rational vertices; that the generic
rotation set in the Hausdorff topology has infinitely many extreme points,
accumulating on a single totally irrational extreme point at which there is a
unique supporting line; and that, although varies continuously with
, the set of extreme points of does not. The family also provides
examples of rotation sets for which an extreme point is not represented by any
minimal invariant set, or by any directional ergodic measure.Comment: Author's accepted version. The final publication is available at
Springer via http://dx.doi.org/10.1007/s00222-015-0628-
Inverse limits as attractors in parameterized families
We show how a parameterized family of maps of the spine of a manifold can be
used to construct a family of homeomorphisms of the ambient manifold which have
the inverse limits of the spine maps as global attractors. We describe
applications to unimodal families of interval maps, to rotation sets, and to
the standard family of circle maps.Comment: 11 pages, 1 figur
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