Seminários de Sistemas Dinâmicos 2026/2

SEMINÁRIOS DE SISTEMAS DINÂMICOS - 2026/2

Coordenador: Prof Rony Cristiano

Seminário 2: 08/09/2026

Palestrante: Samuel Carlos de Souza Ferreira (Ex-Aluno do PPGMAT-IME)

Data: 08/09/2026

Horário: 10h

Local: Auditório do IME

Title: Oscillatory regimes in resonant symmetric 3D piecewise-linear Filippov systems

Abstract: (Resumo em PDF)

This presentation classifies the oscillatory regimes of simple period in a resonant symmetric class of three-dimensional piecewise-linear Filippov systems \(Z=(X,Y)\). The two affine vector fields are related by an involution, and the switching plane contains a visible--visible two-fold singularity. In canonical coordinates, the complex-conjugate eigenvalues of one side are \(C\pm i\), with \(C>0\), the real eigenvalue is \(-2C\), and \(H\) measures the inclination of the corresponding focal line on the switching plane. For every fixed \(C\), an open interval \(\mathcal I_C\) is obtained such that a crossing periodic orbit of simple period exists if and only if \(H\in\mathcal I_C\). Every periodic orbit of simple period in the class is symmetric, and for each admissible parameter value this orbit is unique within the simple-period class. Its half-period parametrizes \(\mathcal I_C\) bijectively and therefore recovers, from the system parameters, the crossing points, the orbit, its period, and its transverse spectral data. The proof uses symmetry to express the full return as the square of a half-return map, whereas resonance supplies polynomial first integrals whose matching confines the closure problem to a conic on the switching plane. The resulting half-return representation also shows that every classified orbit is isolated, hyperbolic, and orbitally asymptotically stable. The two ends of the parameter interval correspond respectively to grazing and to a \(+1\) spectral boundary reached only at infinite amplitude. As a standard consequence of this hyperbolicity and of the fact that the two intersections with \(\Sigma\) lie in the interior of the crossing region, each fixed finite-amplitude cycle admits a unique nearby hyperbolic attracting continuation under sufficiently small sidewise \(C^1\) perturbations. A circuit realization expresses the classified parameter region through explicit component relations.

Seminário 1: 25/08/2026

Palestrante: Leonardo Billioti ( Univ. de Parma- Itália)

Data: 25/08/2026

Horário: 10h

Local: Sala de aula do IME

Title: Complex structures on product manifolds

Abstract: In a classical article by Calabi and Eckmann, it is shown that the product of two spheres of odd dimension, admits an integrable complex structure but does not admit a Kaher structure by cohomological reason. We generelaze this construction by using the momentum map associated to Hamiltonian actions on Kahler manifolds (joint work with Alessandro Minuzzo)

Seminários anteriores:

Seminários de Sistemas Dinâmicos 2026-1

Seminários de Sistemas Dinâmicos 2025-1

Seminários de Sistemas Dinâmicos 2024-2

Seminários de Sistemas Dinâmicos 2024-1

Seminários de Sistemas Dinâmicos 2023-2

Seminários de Sistemas Dinâmicos 2023-1

Seminários de Sistemas Dinâmicos 2022-2

Seminários de Sistemas Dinâmicos 2022-1

Seminários de Sistemas Dinâmicos 2021-2

Seminários de Sistemas Dinâmicos 2020-2 e 2021-1.

Seminários de Sistemas Dinâmicos 2020-1.