Teruhiko Soma
Coexistence of invariant sets with and without SRB measures in H\'enon family.
Mon, 07/12/2010 - 15:01 — SomNambulAuthors: Teruhiko Soma, Shin Kiriki, Ming-Chia Li
Subjects: Dynamical Systems
AbstractLet $\{f_{a,b}\}$ be the (original) H\'enon family. In this paper, we show
that, for any $b$ near $0$, there exists a closed interval $J_b$ which contains
a dense subset $J'$ such that, for any $a\in J'$, $f_{a,b}$ has a quadratic
homoclinic tangency associated with a saddle fixed point of $f_{a,b}$ which
unfolds generically with respect to the one-parameter family $\{f_{a,b}\}_{a\in
J_b}$. By applying this result, we prove that $J_b$ contains a residual subset
$A_b^{(2)}$ such that, for any $a\in A_b^{(2)}$, $f_{a,b}$ admits the Newhouse
phenomenon.Geometry and topology of geometric limits I.
Wed, 02/24/2010 - 16:01 — SomNambulAuthors: Ken'ichi Ohshika, Teruhiko Soma
Subjects: Geometric Topology
AbstractIn this paper, we are concerned with hyperbolic 3-manifolds $\hyperbolic^3/G$
such that $G$ are geometric limits of Kleinian surface groups isomorphic to
$\pi_1(S)$ for a finite-type hyperbolic surface $S$. In the first of the three
main theorems, we shall show that such a hyperbolic 3-manifold is uniformly
bi-Lipschitz homeomorphic to a model manifold which has a structure called
brick decomposition and is embedded in $S \times (0,1)$.
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