Search results for "Saddle"

showing 10 items of 74 documents

Angular spectrum of diffracted wave fields with apochromatic correction.

2008

We report on compensation of diffraction-induced angular dispersion of ultrashort pulses up to a second order. A strategy for chromatic correction profits from high dispersion of kinoform-type zone plates. Ultraflat dispersion curves rely on a saddle point that may be tuned at a prescribed wavelength. Validity of our approach may reach the few-cycles regime.

Physicsbusiness.industryPhysics::OpticsAtomic and Molecular Physics and OpticsAngular spectrum methodWavelengthOpticsApochromatSaddle pointDispersion (optics)Group delay dispersionChromatic scalebusinessUltrashort pulseOptics letters
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Plane foliations with a saddle singularity

2012

Abstract We study the set of planar vector fields with a unique singularity of hyperbolic saddle type. We found conditions to assure that a such vector field is topologically equivalent to a linear saddle. Furthermore, we describe the plane foliations associated to these vector fields. Such a foliation can be split in two subfoliations. One without restriction and another one that is topologically characterized by means of trees.

Planar vector fieldsSingular foliationsPlane (geometry)Mathematical analysisPlanar vector fieldsType (model theory)SingularityFoliation (geology)Vector fieldGeometry and TopologyTopological conjugacySaddleMathematicsSaddle singularityTopology and its Applications
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Blenders near polynomial product maps of $\mathbb C^2$

2021

In this paper we show that if $p$ is a polynomial which bifurcates then the product map $(z,w)\mapsto(p(z),q(w))$ can be approximated by polynomial skew products possessing special dynamical objets called blenders. Moreover, these objets can be chosen to be of two types : repelling or saddle. As a consequence, such product map belongs to the closure of the interior of two different sets : the bifurcation locus of $H_d(\mathbb P^2)$ and the set of endomorphisms having an attracting set of non-empty interior. In an independent part, we use perturbations of H\'enon maps to obtain examples of attracting sets with repelling points and also of quasi-attractors which are not attracting sets.

PolynomialEndomorphismMathematics::Dynamical SystemsMathematics - Complex VariablesApplied MathematicsGeneral Mathematics010102 general mathematicsClosure (topology)BlendersattractorsDynamical Systems (math.DS)01 natural sciencesSet (abstract data type)CombinatoricsBifurcation locusProduct (mathematics)AttractorFOS: MathematicsComplex Variables (math.CV)0101 mathematics[MATH]Mathematics [math]Mathematics - Dynamical SystemsbifurcationsSaddleMathematics
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Performance of a historical cantilever reinforced concrete bridge with half-joint degradation

2022

The lack of maintenance of roadway concrete bridges built from the Second World War until the 70 s of the 20th century has led in recent years to an ever-increasing request for safety assessments. When bridge performance in terms of Serviceability Limit State (SLS) and Ultimate Limit State (ULS) has to be evaluated, in-situ visual inspections and load tests for safety and maintenance assessment have to be coupled with structural analysis. In order to identify a sound bridge structural model and to assess the actual conservation state, more refined models than those usually considered for section and reinforcement design should be used to reproduce the results of load tests and perform globa…

PrestressingHalf-jointStrut-and-tie modelsBuilding and ConstructionServiceabilityCantilever bridgeStructural assessmentCorrosionReinforced concreteGerber saddleCantilever bridge; Corrosion; Gerber saddle; Half-joint; Prestressing; Reinforced concrete; Serviceability; Structural assessment; Strut-and-tie modelsArchitectureSafety Risk Reliability and QualityCivil and Structural EngineeringStructures
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Finite cyclicity of some center graphics through a nilpotent point inside quadratic systems

2015

In this paper we introduce new methods to prove the finite cyclicity of some graphics through a triple nilpotent point of saddle or elliptic type surrounding a center. After applying a blow-up of the family, yielding a singular 3-dimensional foliation, this amounts to proving the finite cyclicity of a family of limit periodic sets of the foliation. The boundary limit periodic sets of these families were the most challenging, but the new methods are quite general for treating such graphics. We apply these techniques to prove the finite cyclicity of the graphic $(I_{14}^1)$, which is part of the program started in 1994 by Dumortier, Roussarie and Rousseau (and called DRR program) to show that…

Pure mathematicsCenter (category theory)Boundary (topology)Dynamical Systems (math.DS)Type (model theory)FoliationNilpotentMathematics (miscellaneous)FOS: MathematicsLimit (mathematics)Point at infinityMathematics - Dynamical Systems34C07 37G15SaddleMathematicsTransactions of the Moscow Mathematical Society
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A C1-generic dichotomy for diffeomorphisms: Weak forms of hyperbolicity or infinitely many sinks or sources

2003

We show that, for every compact n-dimensional manifold, n > 1, there is a residual subset of Diff (M) of diffeomorphisms for which the homoclinic class of any periodic saddle of f verifies one of the following two possibilities: Either it is contained in the closure of an infinite set of sinks or sources (Newhouse phenomenon), or it presents some weak form of hyperbolicity called dominated splitting (this is a generalization of a bidimensional result of Mafine [Ma3]). In particular, we show that any Cl-robustly transitive diffeomorphism admits a dominated splitting.

Pure mathematicsClass (set theory)Infinite setMathematics::Dynamical SystemsGeneralizationMathematical analysisClosure (topology)ManifoldMathematics (miscellaneous)DiffeomorphismHomoclinic orbitStatistics Probability and UncertaintySaddleMathematicsAnnals of Mathematics
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Landesman-Lazer type (p, q)-equations with Neumann condition

2020

We consider a Neumann problem driven by the (p, q)-Laplacian under the Landesman-Lazer type condition. Using the classical saddle point theorem and other classical results of the calculus of variations, we show that the problem has at least one nontrivial weak solution.

Pure mathematicsGeneral MathematicsWeak solution010102 general mathematicsNeumann problemcritical pointsaddle point theoremGeneral Physics and AstronomyType (model theory)01 natural sciences(pq)-LaplacianSaddle point theorem010101 applied mathematicsType conditionSettore MAT/05 - Analisi MatematicaNeumann boundary condition0101 mathematicsLandesman-Lazer type conditionMathematicsActa Mathematica Scientia
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Singular levels and topological invariants of Morse Bott integrable systems on surfaces

2016

Abstract We classify up to homeomorphisms closed curves and eights of saddle points on orientable closed surfaces. This classification is applied to Morse Bott foliations and Morse Bott integrable systems allowing us to define a complete invariant. We state also a realization Theorem based in two transformations and one generator (the foliation of the sphere with two centers).

Pure mathematicsIntegrable systemApplied Mathematics010102 general mathematicsMathematical analysisMorse code01 natural scienceslaw.inventionlawSaddle point0103 physical sciencesFoliation (geology)Topological invariants010307 mathematical physics0101 mathematicsInvariant (mathematics)Mathematics::Symplectic GeometryEQUAÇÕES DIFERENCIAIS ORDINÁRIASAnalysisCircle-valued Morse theoryMorse theoryMathematics
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Transition structures for hydride transfer reactions in vacuo and their role in enzyme catalysis

1996

A general discussion as to the role of in vacuo transition structure in enzyme catalysis is presented. Quantum mechanical aspects are emphasized. The transition structures defined as saddle points ...

Quantitative Biology::BiomoleculesChemistryComputational chemistryHydrideQuantitative Biology::Molecular NetworksSaddle pointDehydrogenasePhysical and Theoretical ChemistryCondensed Matter PhysicsBiochemistryQuantumEnzyme catalysisJournal of Molecular Structure: THEOCHEM
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Applicazione delle Linee guida italiane alle valutazioni di sicurezza strutturale del ponte Corleone sulla tangenziale di Palermo

2022

The "nominal life" of a large part of existing reinforced and prestressed concrete bridges, in Italy, is expiring, often in the absence of ordinary or extraordinary maintenance. Consequently, the Italian infrastructural network is in a critical phase, followed by the alarmed awareness of the public opinion, especially after the collapse of the Polcevera viaduct. Specific guidelines on risk classifi-cation, management, safety assessment, monitoring of existing bridges have been issued by the Superior Council of Public Works in 2020, to address the emergency. Between ‘50s and ‘70s of the last century, important examples of reinforced and prestressed concrete bridges were built in Italy by the…

Reinforced concreteexisting bridges arch bridge Gerber saddles
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