The main objective of this conference is to show the recent developments in qualitative theory of differential equations, especially in low dimension, and their applications to different branches of science. Thus, lectures will be devoted to current topics in bifurcation theory, Abelian integrals, control on the number of periodic orbits, Hilbert 16th problem, oscillations of the time function, Abel equations, integrability and related topics.
It is planned the participation of around 50 researchers. The event aims to create a relaxed atmosphere, with few lectures and free time between them for fruitful discussions.
A décima edição da Oficina de Sistemas Dinâmicos (OSD) será realizada no Instituto de Ciências Matemáticas e de Computação da Universidade de São Paulo (ICMC/USP) e no Departamento de Matemática da Universidade Federal de São Carlos (DM/UFSCar), na cidade de São Carlos-SP, entre os dias 1 e 4 de julho de 2019.
O principal objetivo da OSD é reunir pesquisadores e alunos de Pós-Graduação que se dedicam à pesquisa em Teoria Qualitativa e Geométrica das Equações Diferenciais, buscando formar e intensificar um elo permanente e produtivo entre os pesquisadores e estudantes envolvidos.
Polynomial vector fields occur in many areas of applied mathematics such as for example in population dynamics, chemistry, electrical circuits, neural networks, shock waves, laser physics, hydrodynamics, etc. They are also important from the theoretical point of view. Three problems about these systems stated more than one hundred years ago are still open. Theoretical developments in this area of research are bound to shed light on these very hard open problems and have an impact on applications. In recent years a number of new significant results were obtained on families of polynomial vector fields. The goal of this workshop is to focus on these new developments, facilitate scientific exchanges and stimulate further activity in this growing area of research.
Some of the points which will be discussed are the following:
- The algebraic invariant theory of polynomial differential systems.
- Integrability of polynomial differential systems.
- Algorithms for effective computations of algebraic and geometric properties of polynomial vector fields.
- Hilbert’s 16th problem.
- Counting problems on particular solutions of polynomial vector fields.
- Singular perturbations problems occurring in planar slow-fast systems.