Search results for "smooth dynamical systems"

showing 2 items of 2 documents

Recurrence and genericity

2003

We prove a C^1-connecting lemma for pseudo-orbits of diffeomorphisms on compact manifolds. We explore some consequences for C^1-generic diffeomorphisms. For instance, C^1-generic conservative diffeomorphisms are transitive. Nous montrons un lemme de connexion C^1 pour les pseudo-orbites des diffeomorphismes des varietes compactes. Nous explorons alors les consequences pour les diffeomorphismes C^1-generiques. Par exemple, les diffeomorphismes conservatifs C^1-generiques sont transitifs.

Pure mathematicsMathematics::Dynamical SystemsRiemann manifold[ MATH.MATH-DS ] Mathematics [math]/Dynamical Systems [math.DS][MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS]Dynamical Systems (math.DS)01 natural sciences37C05 37C20FOS: Mathematics0101 mathematicsMathematics - Dynamical SystemsDynamical system (definition)Mathematics::Symplectic GeometryMathematicsLemma (mathematics)Transitive relationRecurrence relationgeneric properties010102 general mathematicsMathematical analysissmooth dynamical systemsGeneral Medicine16. Peace & justicechain recurrence010101 applied mathematicsconnecting lemmaDiffeomorphism
researchProduct

Coupled systems of non-smooth differential equations

2012

Abstract We study the geometric qualitative behavior of a class of discontinuous vector fields in four dimensions. Explicit existence conditions of one-parameter families of periodic orbits for models involving two coupled relay systems are given. We derive existence conditions of one-parameter families of periodic solutions of systems of two second order non-smooth differential equations. We also study the persistence of such periodic orbits in the case of analytic perturbations of our relay systems. These results can be seen as analogous to the Lyapunov Centre Theorem.

Relay systemsLyapunov functionClass (set theory)Mathematics(all)Relay systemsDifferential equationGeneral MathematicsMathematical analysisOrder (ring theory)Non-smooth dynamical systemsNon smoothsymbols.namesakeReversibilitysymbolsPeriodic orbitsVector fieldMathematicsBulletin des Sciences Mathématiques
researchProduct