Search results for "Limit set"

showing 10 items of 11 documents

Attractors for non-autonomous retarded lattice dynamical systems

2015

AbstractIn this paperwe study a non-autonomous lattice dynamical system with delay. Under rather general growth and dissipative conditions on the nonlinear term,we define a non-autonomous dynamical system and prove the existence of a pullback attractor for such system as well. Both multivalued and single-valued cases are considered.

Statistics and ProbabilityDifferential equations with delayDynamical systems theoryNon-autonomous systemslattice dynamical systemsPullback attractorHamiltonian systemLinear dynamical systemProjected dynamical systemAttractorQA1-939pullback attractorMathematicsNumerical AnalysisApplied MathematicsMathematical analysisdifferential equations with delaynon-autonomous systemsClassical mechanicsLattice dynamical systemsPullback attractorset-valued dynamical systemsSet-valued dynamical systemsLimit setRandom dynamical systemMathematicsAnalysis
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ATTRACTORS FOR A LATTICE DYNAMICAL SYSTEM GENERATED BY NON-NEWTONIAN FLUIDS MODELING SUSPENSIONS

2010

In this paper we consider a lattice dynamical system generated by a parabolic equation modeling suspension flows. We prove the existence of a global compact connected attractor for this system and the upper semicontinuity of this attractor with respect to finite-dimensional approximations. Also, we obtain a sequence of approximating discrete dynamical systems by the implementation of the implicit Euler method, proving the existence and the upper semicontinuous convergence of their global attractors.

Dynamical systems theoryApplied MathematicsModeling and SimulationLattice (order)AttractorMathematical analysisLimit setRandom dynamical systemEngineering (miscellaneous)Backward Euler methodNon-Newtonian fluidMathematicsLinear dynamical systemInternational Journal of Bifurcation and Chaos
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A note on correlation and local dimensions

2015

Abstract Under very mild assumptions, we give formulas for the correlation and local dimensions of measures on the limit set of a Moran construction by means of the data used to construct the set.

Correlation dimensionPure mathematicslocal dimensionfinite clustering propertyGeneral MathematicsApplied Mathematics010102 general mathematicsta111General Physics and AstronomyStatistical and Nonlinear Physics01 natural sciencescorrelation dimension010305 fluids & plasmasSet (abstract data type)CombinatoricsCorrelationmoran constructionMathematics - Classical Analysis and ODEs0103 physical sciencesClassical Analysis and ODEs (math.CA)FOS: Mathematics0101 mathematicsLimit setConstruct (philosophy)Mathematics
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Description of the limit set of Henstock–Kurzweil integral sums of vector-valued functions

2015

Abstract Let f be a function defined on [ 0 , 1 ] and taking values in a Banach space X . We show that the limit set I HK ( f ) of Henstock–Kurzweil integral sums is non-empty and convex when the function f has an integrable majorant and X is separable. In the same setting we give a complete description of the limit set.

Discrete mathematicsHenstock–Kurzweil integralApplied MathematicsMathematics::Classical Analysis and ODEsBanach spaceRiemann integralFunction (mathematics)Separable spacesymbols.namesakeSettore MAT/05 - Analisi MatematicaImproper integralsymbolsHenstock–Kurzweil integral Limit set of integral sums Multifunction Aumann integralLimit setVector-valued functionAnalysisMathematicsJournal of Mathematical Analysis and Applications
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On a Planar Dynamical System Arising in the Network Control Theory

2016

We study the structure of attractors in the two-dimensional dynamical system that appears in the network control theory. We provide description of the attracting set and follow changes this set suffers under the changes of positive parameters µ and Θ.

0301 basic medicineDynamical systems theoryPhase portraitattractor selection020206 networking & telecommunicationsphase portraits02 engineering and technologyDynamical systemnetworks controldynamical systemLinear dynamical system03 medical and health sciences030104 developmental biologyProjected dynamical systemControl theoryModeling and SimulationAttractor0202 electrical engineering electronic engineering information engineeringQA1-939Statistical physicsLimit setRandom dynamical systemAnalysisMathematicsMathematicsMathematical Modelling and Analysis
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Passive time-multiplexing super-resolved technique for axially moving targets

2013

In this paper we present a super-resolving approach for detecting an axially moving target that is based upon a time-multiplexing concept and that overcomes the diffraction limit set by the optics of an imaging camera by a priori knowledge of the high-resolution background in front of which the target is moving. As the movement trajectory is axial, the approach can be applied to targets that are approaching or moving away from the camera. By recording a set of low-resolution images at different target axial positions, the super-resolving algorithm weights each image by demultiplexing them using the high-resolution background image and provides a super-resolved image of the target. Theoretic…

Synthetic aperture radarPhysicsbusiness.industryComputingMethodologies_IMAGEPROCESSINGANDCOMPUTERVISIONsuper-resolutionMultiplexingAtomic and Molecular Physics and Opticstime-multiplexingOpticsComputer Science::Computer Vision and Pattern RecognitionMedical imagingTrajectoryA priori and a posterioriElectrical and Electronic EngineeringLimit setdiffraction limitbusinessAxial symmetryEngineering (miscellaneous)Image resolutionsuper-resolvedApplied Optics
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Free vs. Locally Free Kleinian Groups

2015

Abstract We prove that Kleinian groups whose limit sets are Cantor sets of Hausdorff dimension < < 1 are free. On the other hand we construct for any ε > > 0 an example of a non-free purely hyperbolic Kleinian group whose limit set is a Cantor set of Hausdorff dimension < < 1 + + ε.

[ MATH.MATH-GT ] Mathematics [math]/Geometric Topology [math.GT]0209 industrial biotechnologyPure mathematicsMathematics::Dynamical SystemsGeneral MathematicsMathematics::General TopologyGroup Theory (math.GR)02 engineering and technology01 natural sciencesMathematics - Geometric Topology020901 industrial engineering & automationDimension (vector space)[MATH.MATH-GT]Mathematics [math]/Geometric Topology [math.GT]FOS: MathematicsLimit (mathematics)topologia0101 mathematicsMathematicsApplied Mathematics010102 general mathematicsryhmäteoriaGeometric Topology (math.GT)16. Peace & justiceMathematics::Geometric TopologyKleinian groupsCantor setTheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGESHausdorff dimensionComputingMethodologies_DOCUMENTANDTEXTPROCESSINGLimit setMathematics - Group Theory
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The Kuratowski convergence and connected components

2012

International audience; We investigate the Kuratowski convergence of the connected components of the sections of a definable set applying the result obtained to semialgebraic approximation of subanalytic sets. We are led to some considerations concerning the connectedness of the limit set in general. We discuss also the behaviour of the dimension of converging sections and prove some general facts about the Kuratowski convergence in tame geometry.

Connected componentDiscrete mathematicsSocial connectednessApplied Mathematics010102 general mathematicsDimension (graph theory)Mathematics::General Topology16. Peace & justiceKuratowski convergencesubanalytic sets01 natural sciencesKuratowski's theoremKuratowski convergence010101 applied mathematicsDefinable setMathematics::Logictame geometry0101 mathematicsLimit set[MATH]Mathematics [math]Kuratowski closure axiomsAnalysisMathematics
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Surface homeomorphisms with zero dimensional singular set

1998

We prove that if f is an orientation-preserving homeomorphism of a closed orientable surface M whose singular set is totally disconnected, then f is topologically conjugate to a conformal transformation.

Surface (mathematics)Pure mathematics[MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS][ MATH.MATH-DS ] Mathematics [math]/Dynamical Systems [math.DS]Conformal mapDynamical Systems (math.DS)01 natural sciencesKérékjártós theorySet (abstract data type)Totally disconnected spaceRegular homeomorphisms0103 physical sciencesFOS: Mathematics54H20; 57S10; 58FxxRiemann sphereMathematics - Dynamical Systems0101 mathematicsMathematics - General TopologyMathematics010102 general mathematicsGeneral Topology (math.GN)Zero (complex analysis)Applications conformesHomeomorphismHoméomorphismes des surfacesApplications conformes.Transformation (function)Limit set010307 mathematical physicsGeometry and Topology54H20 (Primary) 57S10 (Secondary) 58Fxx (Secondary)Topological conjugacy
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Some Applications of the Poincaré-Bendixson Theorem

2021

We consider a C 1 vector field X defined on an open subset U of the plane, with compact closure. If X has no singular points and if U is simply connected, a weak version of the Poincaré-Bendixson Theorem says that the limit sets of X in U are empty but that one can defined non empty extended limit sets contained into the boundary of U. We give an elementary proof of this result, independent of the classical Poincaré-Bendixson Theorem. A trapping triangle T based at p, for a C 1 vector field X defined on an open subset U of the plane, is a topological triangle with a corner at a point p located on the boundary ∂U and a good control of the tranversality of X along the sides. The principal app…

2010 Mathematics Subject Classification. Primary: 34C05trapping triangles[MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS]separatrix[MATH.MATH-DS] Mathematics [math]/Dynamical Systems [math.DS]Secondary: 34A26 weak Poincaré-Bendixson Theoremextended limit sets[MATH] Mathematics [math][MATH]Mathematics [math]
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