| Full text | |
| Author(s): |
Pereira, Pedro C. C. R.
;
Novaes, Douglas D.
;
Candido, Murilo R.
Total Authors: 3
|
| Document type: | Journal article |
| Source: | JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES; v. 177, p. 45-pg., 2023-09-01. |
| Abstract | |
Determining the existence of compact invariant manifolds is a central quest in the qualitative theory of differential equations. Singularities, periodic solutions, and invariant tori are examples of such invariant manifolds. A classical and useful result from the averaging theory relates the existence of isolated periodic solutions of non-autonomous periodic differential equations, given in a specific standard form, with the existence of simple singularities of the so-called guiding system, which is an autonomous differential equation given in terms of the first non-vanishing higher order averaged function. In this paper, we provide an analogous result for the existence of invariant tori. Namely, we show that a non-autonomous periodic differential equation, given in the standard form, has a normally hyperbolic invariant torus in the extended phase space provided that the guiding system has a hyperbolic limit cycle. We apply this result to show the existence of normally hyperbolic invariant tori in a family of jerk differential equations.& COPY; 2023 Elsevier Masson SAS. All rights reserved. (AU) | |
| FAPESP's process: | 19/05657-4 - Bifurcations of nested invariant tori and invariant sets of Lotka-Volterra differential systems |
| Grantee: | Murilo Rodolfo Cândido |
| Support Opportunities: | Scholarships abroad - Research Internship - Post-doctor |
| 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 |
| FAPESP's process: | 18/07344-0 - Invariant Sets in differential Dynamical Systems: Periodic orbits, Invariant Tori and Algebraic surfaces. |
| Grantee: | Murilo Rodolfo Cândido |
| Support Opportunities: | Scholarships in Brazil - Post-Doctoral |
| 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: | 21/10606-0 - On limit cycles in piecewise linear vector fields with algebraic discontinuity variety |
| Grantee: | Douglas Duarte Novaes |
| Support Opportunities: | Scholarships abroad - Research |
| 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 |