M. J. Pacifico
Exponential speed of mixing for skew-products with singularities.
Mon, 02/13/2012 - 15:01 — SomNambulAuthors: M. J. Pacifico, R. Markarian, J. Vieitez
Subjects: Dynamical Systems
AbstractLet $f: [0,1]\times [0,1] \setminus {1/2} \to [0,1]\times [0,1]$ be the
$C^\infty$ endomorphism given by $$f(x,y)=(2x- [2x], y+ c/|x-1/2|- [y+
c/|x-1/2|]),$$ where $c$ is a positive real number. We prove that $f$ is
topologically mixing and if $c>1/4$ then $f$ is mixing with respect to Lebesgue
measure. Furthermore we prove that the speed of mixing is exponential.Multidimensional Rovella-like attractors.
Tue, 09/08/2009 - 12:16 — SomNambulAuthors: V. Araujo, A. Castro, M. J. Pacifico, V. Pinheiro
Subjects: Dynamical Systems
AbstractWe present a multidimensional flow exhibiting a Rovella-like attractor: a
transitive invariant set with a non-Lorenz-like singularity accumulated by
regular orbits and a multidimensional non-uniformly expanding invariant
direction. Moreover, this attractor has a physical measure with full support
but persists along certain0909.1033 submanifolds of the space of vector fields.
As in the 3-dimensional Rovella-like attractor, this example is not robust.Multidimensional Rovella-like attractors.
Tue, 09/08/2009 - 12:16 — SomNambulAuthors: V. Araujo, A. Castro, M. J. Pacifico, V. Pinheiro
Subjects: Dynamical Systems
AbstractWe present a multidimensional flow exhibiting a Rovella-like attractor: a
transitive invariant set with a non-Lorenz-like singularity accumulated by
regular orbits and a multidimensional non-uniformly expanding invariant
direction. Moreover, this attractor has a physical measure with full support
but persists along certain0909.1033 submanifolds of the space of vector fields.
As in the 3-dimensional Rovella-like attractor, this example is not robust.
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