Topological and metric fixed point theories with application to dynamical systems
18 Out 2022 - 00:00:00
Aula 1, Facultade de Matemáticas USC
"Topological and metric fixed point theories with application to dynamical systems", impartido por Jan Andres, Department of Mathematical Analysis and Applications of Mathematics (Palacký University). Olomouc, República Checa.
Data: 18, 19 e 20 de outubro
Hora: De 10:00 a 12:00 h.
Lugar: Aula 1, Facultade de Matemáticas USC
Duración: 6 horas (presenciais)
The course will consist of three following lectures:
- From Bolzano´s theorem to a multivalued version of the Sharkovsky cycle coexistence theorem.
- From Banach ´s theorem to multivalued fractals,
- From some standard fixed point theorems to degree arguments for multivalued maps.
By metric fixed point theory are meant Banach-type fixed point theorems like the Lifschitz theorem, the Covitz-Nadler theorem, etc., while by topological fixed point theory are meant Schauder-type fixed point theorems like the Lefschetz theorem,the Granas theorem, the Kakutani-Fan theorem, etc. Apart from the sole existence of fixed points, we shall also introduce the Nielsen fixed point theory for multiplicity results, both in the single-valued as well as multivalued cases. In the frame of topological fixed point theory, we will also mention some degree extensions. These fixed point priciples will be applied to differential equations and inclusions in the form of illustrative examples. These applications can possibly deal with e.g. a dry friction problem, or so.
Actividade co-financiada coa colaboración da Consellería de Cultura, Educación, Formación Profesional e Universidades