Families of periodic orbits in resonant reversible systems

Author(s)

Silva Lima, Mauricio Firmino ^[1] ; Teixeira, Marco Antonio ^[2]

Affiliation

^[1] Univ Fed ABC, CMCC, Santo Andre, SP - Brazil

^[2] Univ Estadual Campinas, Dept Matemat, BR-13083970 Campinas, SP - Brazil

• Document type: Journal article
• Source: BULLETIN OF THE BRAZILIAN MATHEMATICAL SOCIETY; v. 40, n. 4, p. 511-537, DEC 2009.
• Web of Science Citations: 4

Abstract

We study the dynamics near an equilibrium point p(0) of a Z(2)(R)- reversible vector field in R(2n) with reversing symmetry R satisfying R(2) = I and dim Fix (R) = n. We deal with one-parameter families of such systems X(lambda) such that X(0) presents p(0) a degenerate resonance of type 0: p: q. We are assuming that the linearized system of X(0) (at p(0)) has eigenvalues: lambda(1) = 0 and lambda(j) = +/- i alpha(j), j = 2,...n. Our main concern is to find conditions for the existence of one-parameter families if periodic orbits near the equilibrium. (AU)

• FAPESP's process: 07/06896-5 - Geometry of control, dynamical and stochastic systems
• Grantee: Luiz Antonio Barrera San Martin
• Support Opportunities: Research Projects - Thematic Grants