Seminário de Sistemas Dinâmicos 2025/1
SEMINÁRIOS DE SISTEMAS DINÂMICOS - 2025/1
Coordenadora dos seminários: Profa. Kamila da Silva Andrade
Todos os seminários serão transmitidos através do link: https://meet.google.com/duf-evfu-mgb
Seminários
Programação
Seminário 1: 18/03/2025
Título do seminário: Generic Bifurcation of Symmetric Two-Zone Piecewise Vector Fields on R³
Ministrante: Prof. Dr. João Carlos da Rocha Medrado - IBILCE/UNESP
Data: 18/03/2025
Horário: 10h
Local: Pelo link acima
Resumo: Following Smale's Program, near symmetric singularities, we characterize the set of generic bifurcation of symmetric two-zone piecewise vector fields on R³. We give the intrinsic conditions and normal forms of these vector fields such that they are of codimensions zero and one.
Joint work with U. Castro.
Seminário 2: 25/03/2025
Título do seminário: Piecewise Smooth Vector Fields where the Switching Manifold is a Double Discontinuous
Ministrante: Dr. Mayk Joaquim dos Santos - Egresso PPGMAT-IME-UFG
Data: 25/03/2025
Horário: 10h
Local: Auditório do IME e pelo link acima
Resumo: At the seminary, main purpose exhibit the open and dense subset of piecewise smooth vector fields that is structural stable in 2D, following the Thom-Smale's program, where the switching manifold is a double discontinuity and therefore the Filippov's convention is not applied.
Seminário 3: 01/04/2025
Título do seminário: Perturbing periodic integral manifold of non-smooth differential systems
Ministrante: Dr. Oscar Alexander Ramírez Cespedes - Universidad Distrital Franciso José de Caldas - Bogotá/Colômbia
Data: 01/04/2025
Horário: 10h
Local: Pelo link acima
Resumo: This talk addresses the perturbation of higher-dimensional non-smooth autonomous differential systems characterized by two zones separated by a codimension-one manifold, with an integral manifold foliated by crossing periodic solutions. Our primary focus is on developing the Melnikov method to analyze the emergence of limit cycles originating from the periodic integral manifold. While previous studies have explored the Melnikov method for autonomous perturbations of non-smooth differential systems with a linear switching manifold and with a periodic integral manifold, either open or of codimension 1, our work extends to non-smooth differential systems with a non-linear switching manifold and more general periodic integral manifolds, where the persistence of periodic orbits is of interest. We illustrate our findings through several examples, highlighting the applicability and significance of our main result.
Seminário 4: 08/04/2025
Título do seminário: Generic upper bounds of cyclicity problem
Ministrante 2: Dr. Yovani Villanueva - IME/UFG
Data: 08/04/2025
Horário: 9h30
Local: Auditório do IME e pelo link acima
Resumo: Hilbert’s 16th problem remains without a definitive solution, even for quadratic systems, and the center-focus problem has also proven elusive for polynomial vector fields of degree $n \geq 3$. In this talk, I provide novel results to get a local analytic first integral of a singularity at the origin, using Lyapunov formula and computer-assisted tools, for generic polynomial differential systems with center linearization in $\mathbb{R}^2$. From those results, upper bounds for the maximum number of center conditions and small limit cycles are obtained, in polynomial vector fields of any finite degree at the origin.
Título do seminário: Limit cycles for piecewise rigid systems with homogeneous non-linearities
Ministrante 1: Dr. Joan Torregrosa - Universitat Autònoma de Barcelona
Data: 08/04/2025
Horário: 10h30
Local: Auditório do IME e pelo link acima
Resumo: The study of limit cycles in piecewise systems can be approached by analyzing the composition of the return map in each region. In fact, this problem can be reinterpreted as the study of the fixed points of the composition of k distinct diffeomorphisms. However, in general, this problem is quite challenging, often intractable, because the diffeomorphisms associated with the return maps are not explicitly known. To make progress, we will consider a special case where all k diffeomorphisms have explicit forms. Our primary focus will be to determine the maximum number of fixed points and investigate their stability. These fixed points can also be viewed as the zeros of the difference map. In this talk, we will present results from both local and global perspectives. Specifically, we will demonstrate how the problem can be studied in the perturbative near-identity case, focusing on the search for higher multiplicity zeros and their unfoldings. We will employ techniques from the qualitative theory of differential equations that are particularly useful in this context.
The talk is based in a current joint work with Armengol Gasull.
Seminário 5: 15/04/2025
Título do seminário: Conley’s theory in the study of Filippov vector fields
Ministrante 2: Ma. Letícia Cândido - IMECC/Unicamp
Data: 15/04/2025
Horário: 10h00
Local: Pelo link acima
Resumo: A Teoria de Conley é uma poderosa ferramenta na análise qualitativa de sistemas dinâmicos, oferecendo uma estrutura topológica baseada no conceito de conjuntos invariantes isolados e nos chamados índices de Conley. Esses conceitos permitem uma compreensão mais profunda da estrutura global do espaço de fases, mesmo na ausência de soluções explícitas.
Nos últimos anos, tem havido um crescente interesse na aplicação da Teoria de Conley a sistemas não suaves, como os campos de Filippov, que descrevem sistemas dinâmicos com descontinuidades. Esses campos surgem naturalmente em diversas áreas, como controle, eletrônica, economia e mecânica com impacto.
A adaptação da Teoria de Conley para campos de Filippov envolve o desenvolvimento de ferramentas conceituais e computacionais que levem em conta o comportamento nas superfícies de descontinuidade. Isso inclui a extensão do conceito de fluxo semifluxo, a definição adequada de conjuntos invariantes e a construção de índices que reflitam a complexidade da dinâmica na região de descontinuidade.
O estudo dessa interação entre topologia e sistemas não suaves contribui para o avanço teórico e prático na análise de sistemas dinâmicos com descontinuidades.
Seminário 6: 22/04/2025
Título do seminário: Results about structural stability and the existence of limit cycles for piecewise smooth linear differential equations separated by the unit circle
Ministrante 2: Dra. Mayara Duarte de Araujo Caldas - UFRJ
Data: 22/04/2025
Horário: 10h00
Local: Pelo link acima
Resumo: In this talk, we investigate the structural stability and the existence of limit cycles in families of piecewise smooth differential equations where the unit circle serves as the discontinuity region. Our study encompasses families featuring singularities of center or saddle type, both visible and invisible, as well as those without any singularities. For the family that admits only constant vector fields, we describe the dynamics over and present a result regarding structural stability. For the other families, we provide an upper bound for the number of limit cycles and present examples that illustrate the maximum number of limit cycles that can be realized.
Seminário 7: 29/04/2025
Título do seminário: Hidden Dynamics: resolving singularities and raising new mysteries
Ministrante 2: Dr. Mike Jeffrey - University of Bristol
Data: 29/04/2025
Horário: 10h00
Local: Pelo link acima
Resumo: Discontinuities are inescapable in modelling dynamical systems, particularly in engineering and biology, anywhere afflicted by switches, decisions, impacts, or cell division. Despite a century of work developing the theory of these “nonsmooth” dynamics systems, two big challenges remain: indeterminacy (equations are non-unique at a discontinuity), and a curse of dimensionality (every new dimension brings new classification problems, so there can be no general theory in n-dimensions as we have for smooth systems).
I will describe how ‘hidden dynamics’ partially resolves this, allowing us to study nonsmooth systems using methods from smooth theory, trying to remove the curse of dimensionality. Also, whereas many current theoretical works try to banish indeterminacy from nonsmooth dynamics, hidden dynamics shows that it is essential, as it also allows us to resolve some singularities, while revealing others that render systems highly unpredictable. I’ll introduce a singularity that challenges our ideas of structural stability of nonsmooth systems, and might hide in the mathematics of the decisions we make every day.
Seminários anteriores:
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.
Seminários de Sistemas Dinâmicos 2019.
Seminários de Sistemas Dinâmicos 2018.
Seminários de Sistemas Dinâmicos 2017.
Seminários de Sistemas Dinâmicos 2016.
Seminários de Sistemas Dinâmicos 2015.
Seminários de Sistemas Dinâmicos 2014.