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

u/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; 1 309 (Sci. 1 Bldg. 309)

u/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; wA A440 (Sci. Bldg. A, A440)

u/speakerF Carlos Cabrera (UNAM, Mexico)
^Cg/titleF Poincare extension of rational maps (2).

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

u/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; wA A440 (Sci. Bldg. A, A440)

u/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; wA A440 (Sci. Bldg. A, A440)

u/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; 1 109 (Sci. 1 Bldg. 109)

u/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; wA A440 (Sci. Bldg. A, A440)

u/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; wA A440 (Sci. Bldg. A, A440)

u/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; wA A440 (Sci. Bldg. A, A440)

u/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.