Search results for "orbits"

showing 5 items of 35 documents

Period-multiplying bifurcations and multifurcations in conservative mappings

1983

The authors have investigated numerically and analytically the period-doubling bifurcations and multifurcations of the periodic orbits of the conservative sine-Gordon mappings. They have derived a general equation for the appearance of multifurcations in conservative mappings. In agreement with many recent studies, they also find evidence that such mappings possess universality properties. They also discuss the role of multifurcations in conservative mappings exhibiting chaotic behaviour.

Pure mathematicsGeneral equationChaoticGeneral Physics and AstronomyPeriodic orbitsStatistical and Nonlinear PhysicsMathematical PhysicsMathematical physicsUniversality (dynamical systems)MathematicsJournal of Physics A: Mathematical and General
researchProduct

The Fatou coordinate for parabolic Dulac germs

2017

We study the class of parabolic Dulac germs of hyperbolic polycycles. For such germs we give a constructive proof of the existence of a unique Fatou coordinate, admitting an asymptotic expansion in the power-iterated log scale.

Pure mathematicsMonomialClass (set theory)Mathematics::Dynamical SystemsConstructive proofLogarithmTransseries[MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS]orbitsDulac germAsymptotic expansionDynamical Systems (math.DS)01 natural sciencesMSC: 37C05 34C07 30B10 30B12 39A06 34E05 37C10 37C1537C05 34C07 30B10 30B12 39A06 34E05 37C10 37C15Mathematics::Algebraic GeometryFOS: Mathematics0101 mathematicsMathematics - Dynamical SystemsMathematicsDulac germ ; Fatou coordinate ; Embedding in a flow ; Asymptotic expansion ; TransseriesdiffeomorphismsMathematics::Complex VariablesApplied Mathematics010102 general mathematicsFatou coordinate010101 applied mathematicsclassificationnormal formsepsilon-neighborhoodsEmbedding in a flowAsymptotic expansionAnalysis
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

Orbital Structure of the Two Fixed Centres Problem

1999

The set of orbits of the Two Fixed Centres problem has been known for a long time (Charlier, 1902, 1907; Pars, 1965), since it is an integrable Hamiltonian system.

Set (abstract data type)Equilibrium pointPhysicsHamiltonian mechanicssymbols.namesakeClassical mechanicsIntegrable systemStructure (category theory)symbolsPeriodic orbitsCelestial mechanicsHamiltonian system
researchProduct

Corrigendum to “Smooth and non-smooth traveling wave solutions of some generalized Camassa–Holm equations” [19 (6) (2014) 1746–1769]

2015

Corrigendum Corrigendum to ‘‘Smooth and non-smooth traveling wave solutions of some generalized Camassa–Holm equations’’ [19 (6) (2014) 1746–1769] M. Russo , S. Roy Choudhury , T. Rehman , G. Gambino b University of Central Florida, Department of Mathematics, 4000 Central Florida Blvd., Orlando, USA University of Palermo, Department of Mathematics and Computer Science, Via Archirafi 34, 90123 Palermo, Italy

Traveling waveNumerical AnalysisCamassa–Holm equationHomoclinic and heteroclinic orbitsApplied MathematicsModeling and SimulationMathematical analysisTraveling waveNon smoothGeneralized Camassa–Holm equationCommunications in Nonlinear Science and Numerical Simulation
researchProduct