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2013 / 11 / 14 (Thu) 16:30 -- 18:00; —Šw•”AŠู A428†Žบ(Sci. Bldg. A428)

œ u‰‰Žา/speakerF Yi-Chiuan Chen (Academia Sinica, Taiwan)
œ ƒ^ƒCƒgƒ‹/titleF Topological Horseshoe in Travelling Waves of Discretized KdV-Burgers-KS Type Equations
œ ƒAƒuƒXƒgƒ‰ƒNƒg/abstractF 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†Šู 309†Žบ (Sci. 1 Bldg. 309)

œ u‰‰Žา/speakerF Yi-Chiuan Chen (Academia Sinica, Taiwan)
œ ƒ^ƒCƒgƒ‹/titleF A Note on Holomorphic Shadowing for H\'enon Maps
œ ƒAƒuƒXƒgƒ‰ƒNƒg/abstractF 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; —Šw•”AŠู A440†Žบ (Sci. Bldg. A, A440)

œ u‰‰Žา/speakerF Carlos Cabrera (UNAM, Mexico)
œ ƒ^ƒCƒgƒ‹/titleF Poincare extension of rational maps (2).

2012 / 07 / 26 (Thu) 15:00 -- 17:00; —Šw•”AŠู A440†Žบ (Sci. Bldg. A, A440)

œ u‰‰Žา/speakerF Carlos Cabrera (UNAM, Mexico)
œ ƒ^ƒCƒgƒ‹/titleF On Poincare extensions of rational maps.
œ ƒAƒuƒXƒgƒ‰ƒNƒg/abstractF 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; —Šw•”AŠู A440†Žบ (Sci. Bldg. A, A440)

œ u‰‰Žา/speakerF Carlos Cabrera (UNAM, Mexico)
œ ƒ^ƒCƒgƒ‹/titleF On dynamical Teichmuller spaces
œ ƒAƒuƒXƒgƒ‰ƒNƒg/abstractF 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; —Šw•”AŠู A440†Žบ (Sci. Bldg. A, A440)

œ u‰‰Žา/speakerF Carlos Cabrera (UNAM, Mexico)
œ ƒ^ƒCƒgƒ‹/titleF 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†Šู 109†Žบ (Sci. 1 Bldg. 109)

œ u‰‰Žา/speakerF Davoud Cheraghi (University of Warwick, UK)
œ ƒ^ƒCƒgƒ‹/titleF Trajectories of complex quadratic polynomials with an irrationally indifferent fixed point
œ ƒAƒuƒXƒgƒ‰ƒNƒg/abstractF 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; —Šw•”AŠู A440†Žบ (Sci. Bldg. A, A440)

œ u‰‰Žา/speakerF Carlos Cabrera (UNAM, Mexico)
œ ƒ^ƒCƒgƒ‹/titleF On the topology of the inverse limit of a branched covering over a Riemann surface (3)

2012 / 06 / 22 (Fri) 10:00 -- 12:00; —Šw•”AŠู A440†Žบ (Sci. Bldg. A, A440)

œ u‰‰Žา/speakerF Carlos Cabrera (UNAM, Mexico)
œ ƒ^ƒCƒgƒ‹/titleF On the topology of the inverse limit of a branched covering over a Riemann surface (2)

2012 / 06 / 14 (Thu) 15:00 -- 17:00; —Šw•”AŠู A440†Žบ (Sci. Bldg. A, A440)

œ u‰‰Žา/speakerF Carlos Cabrera (UNAM, Mexico)
œ ƒ^ƒCƒgƒ‹/titleF On the topology of the inverse limit of a branched covering over a Riemann surface (1)
œ ƒAƒuƒXƒgƒ‰ƒNƒg/abstractF 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.

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