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DTSTART;TZID=Europe/Madrid:20230308T120000
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DTSTAMP:20260522T232820
CREATED:20230306T193530Z
LAST-MODIFIED:20230306T193530Z
UID:3071-1678276800-1678279200@iumpa.webs.upv.es
SUMMARY:Conferencia Vinícius V. Fávaro (Universidade Federal de Uberlândia - Brasil)
DESCRIPTION:Linear dynamics of operators on non-metrizable topological vector spaces\nIn this talk we will explore the following notions of chaos for operators on non-metrizable topological vector spaces: mixing\, hypercyclicity\, cyclicity\, n-supercyclicity\, Li-Yorke chaos and Devaney chaos. We will discuss the main differences between these notions for operators on Fréchet and on non-metrizable topological vector spaces. \nTo illustrate some of these differences\, we will explore results about the linear dynamics of convolution operators on spaces of entire functions of finitely and infinitely many complex variables. A classical result due to Godefroy and Shapiro states that every nontrivial convolution operator on the Fréchet space $\mathcal{H}(\mathbb{C}^n)$ of all entire functions of $n$ complex variables is hypercyclic. In sharp contrast to this result\, in a joint work with J. Mujica it was showed that no translation operator on the space $\mathcal{H}(\mathbb{C}^\mathbb{N})$ (which is a complete non-metrizable locally convex space) of entire functions of infinitely many complex variables is hypercyclic. In 2020\, in a joint work with B. Caraballo\, it was showed that no convolution operator on $\mathcal{H}(\mathbb{C}^\mathbb{N})$ is cyclic or $n$-supercyclic for any positive integer $n$. In the opposite direction\, it was proved that every nontrivial convolution operator on $\mathcal{H}(\mathbb{C}^\mathbb{N})$ is mixing. Exploring the concept of Li-Yorke chaos on non-metrizable topological vector spaces\, it was also proved that nontrivial convolution operators on $\mathcal{H}(\mathbb{C}^\mathbb{N})$ are Li-Yorke chaotic. Recently\, we also proved that every nontrivial convolution operator on $\mathcal{H}(\mathbb{C}^\mathbb{N})$ is (Devaney) chaotic.
URL:https://iumpa.webs.upv.es/event/conferencia-vinicius-v-favaro-universidade-federal-de-uberlandia-brasil/
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DTSTART;TZID=Europe/Madrid:20230308T125000
DTEND;TZID=Europe/Madrid:20230308T133000
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CREATED:20230306T193657Z
LAST-MODIFIED:20230306T193657Z
UID:3073-1678279800-1678282200@iumpa.webs.upv.es
SUMMARY:Conferencia Udayan B. Darji (University of Louisville\, EEUU)
DESCRIPTION:Local Entropy and Applications\nIn this talk\, we introduce basic of local entropy theory and discuss how it can be applied in various settings in topological dynamics. We pay particular attention to Uniformly Positive Entropy and Complete Positive Entropy introduced by Blanchard in 90’s. Whereas these notions coincide in measure theoretical dynamics\, they are very different in topological dynamics. \nAll notions will be defined and the talk will be accessible to graduate students.
URL:https://iumpa.webs.upv.es/event/conferencia-udayan-b-darji-university-of-louisville-eeuu/
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