L.J. Diaz
Abundance of $C^1$-robust homoclinic tangencies.
Wed, 09/23/2009 - 13:19 — SomNambulAuthors: L.J. Diaz, C. Bonatti
Subjects: Dynamical Systems
AbstractA diffeomorphism $f$ has a $C^1$-robust homoclinic tangency if there is a
$C^1$-neighbourhood $\cU$ of $f$ such that every diffeomorphism in $g\in \cU$
has a hyperbolic set $\La_g$, depending continuously on $g$, such that the
stable and unstable manifolds of $\La_g$ have some non-transverse intersection.
For every manifold of dimension greater than or equal to three, we exhibit a
local mechanism (blender-horseshoes) generating diffeomorphisms with
$C^1$-robust homoclinic tangencies.Abundance of $C^1$-robust homoclinic tangencies.
Wed, 09/23/2009 - 13:19 — SomNambulAuthors: L.J. Diaz, C. Bonatti
Subjects: Dynamical Systems
AbstractA diffeomorphism $f$ has a $C^1$-robust homoclinic tangency if there is a
$C^1$-neighbourhood $\cU$ of $f$ such that every diffeomorphism in $g\in \cU$
has a hyperbolic set $\La_g$, depending continuously on $g$, such that the
stable and unstable manifolds of $\La_g$ have some non-transverse intersection.
For every manifold of dimension greater than or equal to three, we exhibit a
local mechanism (blender-horseshoes) generating diffeomorphisms with
$C^1$-robust homoclinic tangencies.Non-hyperbolic ergodic measures with large support.
Tue, 09/01/2009 - 12:47 — SomNambulAuthors: Ch. Bonatti, L.J. Diaz, A. Gorodetski
Subjects: Dynamical Systems
AbstractWe prove that there is a residual subset $\mathcal{S}$ in $\text{Diff}^1(M)$
such that, for every $f\in \mathcal{S}$, any homoclinic class of $f$ with
invariant one dimensional central bundle containing saddles of different
indices (i.e. with different dimensions of the stable invariant manifold)
coincides with the support of some invariant ergodic non-hyperbolic (one of the
Lyapunov exponents is equal to zero) measure of $f$.
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