Continuous curves of nonmetric pseudo-arcs and semi-conjugacies to interval maps

Quasi-symmetry of Conjugacies between Interval Maps

Sets of Non-differentiability for Conjugacies between Expanding Interval Maps

We study di erentiability of topological conjugacies between expanding piecewise C1+ interval maps. If these conjugacies are not C1 , then they have zero derivative almost everywhere. We obtain the result that in this case the Hausdor dimension of the set of points for which the derivative of the conjugacy does not exist lies strictly between zero and one. Using multifractal analysis and thermo...

Conjugacies between Rational Maps and Extremal Quasiconformal Maps

We show that two rational maps which are K-quasiconformally combinatorially equivalent are K-quasiconformally conjugate. We also study the relationship between the boundary dilatation of a combinatorial equivalence and the dilatation of a conjugacy. The Teichmüller theory is a powerful tool in the study of complex analytic dynamics. In addition to the work of D. Sullivan [Su] and W. Thurston (r...

Moment Maps, Pseudo-holomorphic Curves and Symplectomorphism Groups

These are the notes of a 3-lecture mini-course on some basic topics of symplectic geometry and topology, given at the XIV Fall Workshop on Geometry and Physics, September 14–16, 2005, in Bilbao, Spain, to a general mathematical audience.

Pseudo-anosov Maps and Simple Closed Curves on Surfaces

Suppose C and C are two sets of simple closed curves on a hyperbolic surface F . We will give necessary and sufficient conditions for the existence of a pseudo-Anosov map g such that g(C) ∼= C. Pseudo-Anosov maps are the most important class among surface homeomorphisms [Th3], and they play important roles in 3-manifold theory [Th2]. This note is to address the following question: Suppose F is ...