# Analysis, Geometry, and Dynamical Systems Seminar

## Past sessions

Newer session pages: Next 8 7 6 5 4 3 2 1 Newest

### The set of periods for the Morse-Smale diffeomorphisms on ${T}^{2}$

We shall use the Lefschetz zeta function for studying the set of periods of the Morse-Smale diffeomorfisms defined on the 2-dimensional torus for every homotopy class.

### The Baum-Connes conjecture and linear group actions on spaces of finite asymptotic dimension

The Baum-Connes conjecture describes the $K$-theory of a reduced crossed product of a ${C}^{*}$-algebra by a group $G$ in terms of the $K$-homology of the classifying space of proper actions of $G$. We shall describe the Conjecture for discrete group case and its connotations. Commenting on results of Guentner, Higson, Kasparov, Weinberger, and Yu, we investigate the possibility of applying a finite-dimensionality argument in order to prove parts of the Conjecture for discrete linear groups.

### Hausdorff dimension for an open class of repellers in ${ℝ}^{2}$

We compute the Hausdorff dimension for an open class of Iterated Function Schemes in ${ℝ}^{2}$ in the ${C}^{2}$ topology, in terms of the pressure function. This class is characterized by a domination condition that is not too strong, plus the non-overlapping condition. Also in this class there exists a unique invariant probability measure of full Hausdorff dimension. Finally we show that the Hausdorff dimension is a continuous function in this class.

### Bogoliubov functionals: from measure theory to functional analysis

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