| Full text | |
| Author(s): |
Novaes, Douglas D.
;
Pereira, Pedro C. C. R.
Total Authors: 2
|
| Document type: | Journal article |
| Source: | BULLETIN DES SCIENCES MATHEMATIQUES; v. 190, p. 13-pg., 2023-12-19. |
| Abstract | |
Floquet ' s Theorem is a celebrated result in the theory of ordinary differential equations. Essentially, the theorem states that, when studying a linear differential system with Tperiodic coefficients, we can apply a, possibly complex, Tperiodic change of variables that transforms it into a linear system with constant coefficients. In this paper, we explore further the question of the nature of this change of variables. We state necessary and sufficient conditions for it to be real and T-periodic. Failing those conditions, we prove that we can still find a real change of variables that is '' partially '' T-periodic and '' partially '' T-antiperiodic. We also present applications of this new form of Floquet ' s Theorem to the study of the behavior of solutions of nonlinear differential systems near periodic orbits.(c) 2023 Elsevier Masson SAS. All rights reserved. (AU) | |
| FAPESP's process: | 20/14232-4 - Bifurcation of invariant tori of differential systems via higher order averaging theory |
| Grantee: | Pedro Campos Christo Rodrigues Pereira |
| Support Opportunities: | Scholarships in Brazil - Doctorate |
| FAPESP's process: | 18/13481-0 - Geometry of control, dynamical and stochastic systems |
| Grantee: | Marco Antônio Teixeira |
| Support Opportunities: | Research Projects - Thematic Grants |
| FAPESP's process: | 19/10269-3 - Ergodic and qualitative theories of dynamical systems II |
| Grantee: | Claudio Aguinaldo Buzzi |
| Support Opportunities: | Research Projects - Thematic Grants |
| FAPESP's process: | 22/09633-5 - Averaging theory for studying invariant tori and periodic behavior in differential equations and inclusions |
| Grantee: | Douglas Duarte Novaes |
| Support Opportunities: | Regular Research Grants |