| Full text | |
| Author(s): |
Buzzi, Claudio A.
;
Pazim, Rubens
;
Perez-Gonzalez, Set
Total Authors: 3
|
| Document type: | Journal article |
| Source: | Journal of Mathematical Analysis and Applications; v. 445, n. 1, p. 631-649, JAN 1 2017. |
| Web of Science Citations: | 1 |
| Abstract | |
This paper is concerned with 1-parameter families of periodic solutions of piecewise smooth planar vector fields, when they behave like a center of smooth vector fields. We are interested in finding a separation boundary for a given pair of smooth systems in such a way that the discontinuous system, formed by the pair of smooth systems, has a continuum of periodic orbits. In this case we call the separation boundary as a center boundary. We prove that given a pair of systems that share a hyperbolic focus singularity p(0), with the same orientation and opposite stability, and a ray Sigma(0) with endpoint at the singularity p(0), we can find a smooth manifold Omega such that Sigma(0) boolean OR [p(0)] boolean OR Omega is a center boundary. The maximum number of such manifolds satisfying these conditions is five. Moreover, this upper bound is reached. (C) 2016 Elsevier Inc. All rights reserved. (AU) | |
| FAPESP's process: | 13/24541-0 - Ergodic and qualitative theory of dynamical systems |
| Grantee: | Claudio Aguinaldo Buzzi |
| Support Opportunities: | Research Projects - Thematic Grants |