0000000000744328
AUTHOR
Marco Antonio Teixeira
showing 3 related works from this author
Bifurcation of Singularities Near Reversible Systems
1994
In this paper we study generic unfoldings of certain singularities in the class of all C ∞ reversible systems on R 2.
PIECEWISE SMOOTH REVERSIBLE DYNAMICAL SYSTEMS AT A TWO-FOLD SINGULARITY
2012
This paper focuses on the existence of closed orbits around a two-fold singularity of 3D discontinuous systems of the Filippov type in the presence of symmetries.
Periodic solutions of a class of non-autonomous second order differential equations with discontinuous right-hand side
2012
Abstract The main goal of this paper is to discuss the existence of periodic solutions of the second order equation: y ″ + η sgn ( y ) = α sin ( β t ) with ( η , α , β ) ∈ R 3 η > 0 . We analyze the dynamics of such an equation around the origin which is a typical singularity of non-smooth dynamical systems. The main results consist in exhibiting conditions on the existence of typical periodic solutions that appear generically in such systems. We emphasize that the mechanism employed here is applicable to many more systems. In fact this work fits into a general program for understanding the dynamics of non-autonomous differential equations with discontinuous right-hand sides.