Por Daniel Graça (Departamento de Matemática, Faculdade de Ciências e Tecnologia da Universidade do Algarve).

At the beginning of the 20th century, David Hilbert proposed a list of 23 open problems in mathematics which proved to be very influential. The 16th problem consists on two subproblems, the second of which asks for an upper bound on the number of limit cycles that planar polynomial vector fields of degree n can have and an investigation of their relative positions. This problem remains unsolved for all n>1.

In this talk we consider an exact variant of Hilbert's 16th problem, where we will be interested in studying the operator which maps a planar vector field to the exact number of its limit cycles. We will show that, while this operator is in general not computable, it is uniformly computable on a dense subset of C^1 vector fields over the unit ball. This talk describes joint work with Ning Zhong.

Zoom Meeting | ID da reunião: 890 8479 3299 - senha de acesso: 409604