Now showing items 1-10 of 161
Quadratic planar systems with two parallel invariant straight lines
In this paper, we classify the global phase portraits of all quadratic planar systems with two parallel invariant straight lines. The main techniques used are Poincaŕe Compactification and Normal Forms Theory combined with ...
Conjuntos minimais e caóticos em campos de vetores planares suaves por partes
(Universidade Estadual Paulista (Unesp), 2016-01-06)
The main result of this work is the Poincaré - Bendixson Theorem for planar piecewise smooth vector fields, which tell us what kind of limit sets arise in this context. We will also study details about the concepts of ...
Lyapunov coefficients for an invisible fold-fold singularity in planar piecewise Hamiltonian systems
We study the stability of an invisible fold-fold singularity of planar piecewise smooth Hamiltonian vector fields by computing some kind of Lyapunov coefficients. We obtain the general expressions for the first five Lyapunov ...
On the Closing Lemma for planar piecewise smooth vector fields
A large number of papers deal with “Closing Lemmas” for Cr-vector fields (and Cr-diffeomorphisms). Here, we introduce this subject and formalize the terminology about nontrivially recurrent points and nonwandering points ...
Existência e configuração de ciclos limites em sistemas diferenciais planares
(Universidade Federal de Santa MariaBrasilMatemáticaUFSMPrograma de Pós-Graduação em MatemáticaCentro de Ciências Naturais e Exatas, 2018-03-16)
In this dissertation, we present results on the existence of limit cycles in planar differential systems, configuration of such cycles and the dynamics of nonlinear systems near periodic orbits.
Local cyclicity in low degree planar piecewise polynomial vector fields
(Elsevier B.V., 2021-08-01)
In this work, we are interested in isolated crossing periodic orbits in planar piecewise polynomial vector fields defined in two zones separated by a straight line. In particular, in the number of limit cycles of small ...
On pairs of polynomial planar foliations
(Juliusz Schauder Ctr Nonlinear StudiesTorunPolónia, 2007)
Chaotic planar piecewise smooth vector fields with non-trivial minimal sets
In this paper some aspects on chaotic behavior and minimality in planar piecewise smooth vector fields theory are treated. The occurrence of non-deterministic chaos is observed and the concept of orientable minimality is ...
On Poincaré-Bendixson theorem and non-trivial minimal sets in planar nonsmooth vector fields
In this paper some qualitative and geometric aspects of nonsmooth vector felds theory are discussed. A Poincaré-Bendixson Theorem for a class of nonsmooth systems is presented. In addition, a minimal set in planar Filippov ...
Equivalence between the planar Dirac oscillator and a spin-1/2 fermion embedded in a transverse homogeneous magnetic field
(Sociedade Brasileira de Física, 2019-07-10)
It is shown that a spin-1/2 fermion coupled to the axially symmetric electromagnetic vector potential has the same matrix structure as that one for the planar Dirac oscillator. In particular, the planar Dirac oscillator ...