กfอwnZ~i[ / Complex Dynamics Seminar

ผรฎๅwๅw@ฝณศwคศ / Graduate School of Mathematics, Nagoya University

iผรฎwE๓`ฉ็ฬANZXj

ผรฎๅwๅw@ฝณศwคศ / Graduate School of Mathematics, Nagoya University

iผรฎwE๓`ฉ็ฬANZXj

**2013 / 11 / 14 (Thu) 16:30 -- 18:00; wAู A428บ(Sci. Bldg. A428)**

uา/speakerF
Yi-Chiuan Chen (Academia Sinica, Taiwan)

^Cg/titleF
Topological Horseshoe in Travelling Waves of Discretized
KdV-Burgers-KS Type Equations

AuXgNg/abstractF
Applying the concept of anti-integrable limit to space-time
discretized KdV-Burgers-KS type equations, we show that there
exist topological horseshoes in the phase space formed by the
initial states of travelling wave solutions
of the resulted coupled map lattices.
In particular, the coupled map lattices display
spatio-temporal chaos on the horseshoes.

**2012 / 12 / 19 (Wed) 15:00 -- 16:30; 1ู 309บ (Sci. 1 Bldg. 309)**

uา/speakerF
Yi-Chiuan Chen (Academia Sinica, Taiwan)

^Cg/titleF
A Note on Holomorphic Shadowing for H\'enon Maps

AuXgNg/abstractF
In studying the complex H\'enon maps,
Mummert defined an operator the fixed points of which give
rise to bounded orbits. This enabled his to obtain an
estimate of the solenoid locus. Instead of the contraction
mapping theorem, in the talk, I shall present an implicit
function theorem version of his result, with some
generalisation.

**2012 / 08 / 09 (Thu) 15:00 -- 17:00; wAู A440บ (Sci. Bldg. A, A440)**

uา/speakerF
Carlos Cabrera (UNAM, Mexico)

^Cg/titleF
Poincare extension of rational maps (2).

**2012 / 07 / 26 (Thu) 15:00 -- 17:00; wAู A440บ (Sci. Bldg. A, A440)**

uา/speakerF
Carlos Cabrera (UNAM, Mexico)

^Cg/titleF
On Poincare extensions of rational maps.

AuXgNg/abstractF
In this talk we show the existence of geometric Poincar\'e extensions for an open and dense set of rational maps.
Another of our main results is the existence of an extension that applies for the semigroup of Blaschke maps, which is a homomorphism of semigroups.

**2012 / 07 / 19 (Thu) 15:00 -- 17:00; wAู A440บ (Sci. Bldg. A, A440)**

uา/speakerF
Carlos Cabrera (UNAM, Mexico)

^Cg/titleF
On dynamical Teichmuller spaces

AuXgNg/abstractF
Following ideas from a preprint of the Peter Makienko,
we investigate relations of dynamical Teichmuller spaces with dynamical objects.
We also establish some connections with the theory of deformations of inverse limits and laminations in holomorphic dynamics.
This is a joint work with Peter Makienko.

**2012 / 07 / 12 (Thu) 15:00 -- 17:00; wAู A440บ (Sci. Bldg. A, A440)**

uา/speakerF
Carlos Cabrera (UNAM, Mexico)

^Cg/titleF
On the topology of the inverse limit of a branched covering over a Riemann surface (4)

**2012 / 07 / 9 (Mon) 15:00 -- 16:30; 1ู 109บ (Sci. 1 Bldg. 109)**

uา/speakerF
Davoud Cheraghi (University of Warwick, UK)

^Cg/titleF
Trajectories of complex quadratic polynomials
with an irrationally indifferent fixed point

AuXgNg/abstractF
The local, semi-local, and global
dynamics of the complex quadratic polynomials $P_\alpha(z):=
e^{2\pi i \alpha}z+z^2: \mathbb{C}\to \mathbb{C}$, for
irrational values of $\alpha$, have been extensively studied
through various methods. The main source of difficulty is
the interplay between the tangential movement created by the
fixed point and the radial movement caused by the critical
point. This naturally brings the arithmetic nature of
$\alpha$ into play.
Using a renormalization technique developed by H. Inou and M.
Shishikura, we analyze this interaction, and in particular,
describe the topological behavior of the orbit of typical
points under these maps.

**2012 / 07 / 5 (Thu) 15:00 -- 17:00; wAู A440บ (Sci. Bldg. A, A440)**

uา/speakerF
Carlos Cabrera (UNAM, Mexico)

^Cg/titleF
On the topology of the inverse limit of a branched covering over a Riemann surface (3)

**2012 / 06 / 22 (Fri) 10:00 -- 12:00; wAู A440บ (Sci. Bldg. A, A440)**

uา/speakerF
Carlos Cabrera (UNAM, Mexico)

^Cg/titleF
On the topology of the inverse limit of a branched covering over a Riemann surface (2)

**2012 / 06 / 14 (Thu) 15:00 -- 17:00; wAู A440บ (Sci. Bldg. A, A440)**

uา/speakerF
Carlos Cabrera (UNAM, Mexico)

^Cg/titleF
On the topology of the inverse limit of a branched covering over a Riemann surface (1)

AuXgNg/abstractF
We introduce the Plaque Topology on the inverse limit of a branched covering map over a Riemann surface to study its dynamical properties. We also consider a Boolean Algebra to compute local topological invariants. With these tools we obtain a description of the points in the inverse limit.