14:00h:-15:00h |
Matinê |
Udayan B. Darji (Univ. of Louisville) |
Linear Dynamics |
RESUMO: Linear dynamics is a relatively recent area of mathematics which lies at the intersection of operator theory and dynamical systems. A flurry of intriguing results have been obtained in this area starting with investigation of transitivity and mixing. Recent investigations include concepts such as Li-Yorke, Devaney and distributional chaos, invariant measures, ergodicity and frequently hypercyclic, expansive, hyperbolic, shadowing and structural stability. In this survey panoramic talk, we will highlight some of the essential results. We will also discuss some of the joint results of the speaker with Bernardes, Cirilo, Messaoudi, Pires, Pujals, Varão and others. |
15:10h-16:10h |
Palestra1 |
Alex M. Zamudio (UFRJ) |
Hausdorff dimension of projections of dynamically defined complex Cantor sets
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)
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Palestra2 |
Khadim War (IMPA) |
Uniqueness of the measure of maximal entropy for geodesic flows on certain manifolds without conjugate points |
RESUMO: We prove that for closed surfaces M with Riemannian metrics without conjugate points and genus than 2 the geodesic flow on the unit tangent bundle has a unique measure of maximal entropy. Furthermore, this measure is fully supported and the flow is mixing with respect to this measure. We formulate conditions under which this result extends to higher dimensions. |
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