Search results for "Manifold"

showing 10 items of 415 documents

INSTABILITY OF HAMILTONIAN SYSTEMS IN THE SENSE OF CHIRIKOV AND BIFURCATION IN A NON LINEAR EVOLUTION PROBLEM EMANATING FROM PHYSICS

2004

We prove the existence of a minimal geometrico-dynamical condition to create hyperbolicity in section in the vicinity of a transversal homoclinic partially hyperbolic torus in a near integrable Hamiltonian system with three degrees of freedom. We deduce in this context a generalization of the Easton's theorem of symbolic dynamics. Then we give the optimal estimation of the Arnold diffusion time along a transition chain in the initially hyperbolic Hamiltonian systems with three degrees of freedom with a surrounding chain of hyperbolic periodic orbits .In a second part, we describe geometrically a mechanism of diffusion studied by Chirikov in a near integrable Hamiltonian system with three de…

[ MATH ] Mathematics [math]dynamique symboliquehyperbolicitymodulational instabilityNavier Stokespartially hyperbolic tori[MATH] Mathematics [math]amplitude equationschevauchement de résonancescenter manifoldconvection mixte –hyperbolicitéoverlapping resonancessymbolic dynamicséquations d'amplitudesystèmes Hamiltoniensbifurcationinstabilité modulationnellevariété centraleHamiltonian systems[MATH]Mathematics [math]tores partiellement hyperboliquesmixed convection
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Finite quotients of the Picard group and related hyperbolic tetrahedral and Bianchi groups

2001

There is an extensive literature on the fi{}nite index subgroups and the fi{}nite quotient groups of the Picard group $PSL\left(2,\mathbb{Z}\mid i\mid\right)$. The main result of the present paper is the classifi{}cation of all linear fractional groups $PSL\left(2,p^{m}\right)$ which occur as fi{}nite quotients of the Picard group. We classify also the fi{}nite quotients of linear fractional type of various related hyperbolic tetrahedral groups which uniformize the cusped orientable hyperbolic 3-orbifolds of minimal volumes. Also these cusped tetrahedral groups are of Bianchi type, that is of the form $PSL\left(2,\mathbb{Z}\mid\omega\mid\right)$ or $PGL\left(2,\mathbb{Z}\mid\omega\mid\right…

[ MATH.MATH-GT ] Mathematics [math]/Geometric Topology [math.GT]20F38hyperbolic 3-orbifold and 3-manifoldhyperbolic tetrahedral group[MATH.MATH-GT]Mathematics [math]/Geometric Topology [math.GT]Picard group57S17Mathematics::Geometric Topology57M60[MATH.MATH-GT] Mathematics [math]/Geometric Topology [math.GT]
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On the classification of Kim and Kostrikin manifolds

2006

International audience; We completely classify the topological and geometric structures of some series of closed connected orientable 3-manifolds introduced by Kim and Kostrikin in [20, 21] as quotient spaces of certain polyhedral 3-cells by pairwise identifications of their boundary faces. Then we study further classes of closed orientable 3-manifolds arising from similar polyhedral schemata, and describe their topological properties.

[ MATH.MATH-GT ] Mathematics [math]/Geometric Topology [math.GT]3-manifolds; group presentations; spines; orbifolds; polyhedral schemata; branched coveringsAlgebra and Number TheorySeries (mathematics)010102 general mathematicsBoundary (topology)spines0102 computer and information sciences01 natural sciencesgroup presentations3-manifoldsCombinatoricspolyhedral schemata010201 computation theory & mathematics[MATH.MATH-GT]Mathematics [math]/Geometric Topology [math.GT]Pairwise comparisonorbifoldsbranched coverings0101 mathematicsQuotient[MATH.MATH-GT] Mathematics [math]/Geometric Topology [math.GT]Mathematics
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Hyperbolic isometries versus symmetries of links

2009

We prove that every finite group is the orientation-preserving isometry group of the complement of a hyperbolic link in the 3-sphere.

[ MATH.MATH-GT ] Mathematics [math]/Geometric Topology [math.GT]Pure mathematicsHyperbolic groupHyperbolic linkTotally geodesic surfaces01 natural sciencesRelatively hyperbolic group57M60Mathematics - Geometric Topology[MATH.MATH-GT]Mathematics [math]/Geometric Topology [math.GT]0103 physical sciencesFOS: Mathematics0101 mathematicsMathematics[MATH.MATH-GT] Mathematics [math]/Geometric Topology [math.GT]Hyperbolic linksHyperbolic space010102 general mathematicsHyperbolic 3-manifoldHyperbolic manifoldGeometric Topology (math.GT)Algebra010307 mathematical physicsGeometry and TopologyIsometry groupHyperbolic Dehn surgeryHyperbolic Dehn surgeryTopology and its Applications
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Conway irreducible hyperbolic knots with two common covers

2005

International audience; For each pair of coprime integers n > m ≥ 2 we construct pairs of non equivalent Conway irreducible hyperbolic knots with the same n-fold and m-fold cyclic branched covers.

[ MATH.MATH-GT ] Mathematics [math]/Geometric Topology [math.GT]Pure mathematicsQuantitative Biology::BiomoleculesCoprime integersHyperbolic groupMathematics::Number TheoryGeneral Mathematics010102 general mathematicsSkein relationHyperbolic 3-manifoldVolume conjecture01 natural sciencesRelatively hyperbolic groupMathematics::Geometric TopologyKnot theoryAlgebra[MATH.MATH-GT]Mathematics [math]/Geometric Topology [math.GT]0103 physical sciences010307 mathematical physics0101 mathematicsMathematics[MATH.MATH-GT] Mathematics [math]/Geometric Topology [math.GT]
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3-manifolds which are orbit spaces of diffeomorphisms

2008

Abstract In a very general setting, we show that a 3-manifold obtained as the orbit space of the basin of a topological attractor is either S 2 × S 1 or irreducible. We then study in more detail the topology of a class of 3-manifolds which are also orbit spaces and arise as invariants of gradient-like diffeomorphisms (in dimension 3). Up to a finite number of exceptions, which we explicitly describe, all these manifolds are Haken and, by changing the diffeomorphism by a finite power, all the Seifert components of the Jaco–Shalen–Johannson decomposition of these manifolds are made into product circle bundles.

[ MATH.MATH-GT ] Mathematics [math]/Geometric Topology [math.GT]Seifert fibrationsClass (set theory)Pure mathematicsGradient-like diffeomorphism[ MATH.MATH-DS ] Mathematics [math]/Dynamical Systems [math.DS]Dimension (graph theory)[MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS][MATH.MATH-DS] Mathematics [math]/Dynamical Systems [math.DS]Space (mathematics)01 natural sciences[MATH.MATH-GT]Mathematics [math]/Geometric Topology [math.GT]0103 physical sciencesAttractorJaco–Shalen–Johannson decomposition0101 mathematicsFinite setMathematics::Symplectic Geometry[MATH.MATH-GT] Mathematics [math]/Geometric Topology [math.GT]Mathematics010102 general mathematicsMathematical analysisMathematics::Geometric Topology3-manifoldsProduct (mathematics)010307 mathematical physicsGeometry and TopologyDiffeomorphismOrbit (control theory)
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Non subanalyticity of sub-Riemannian Martinet spheres

2001

Abstract Consider the sub-Riemannian Martinet structure (M,Δ,g) where M= R 3 , Δ= Ker ( d z− y 2 2 d x) and g is the general gradated metric of order 0 : g=(1+αy) 2 d x 2 +(1+βx+γy) 2 d y 2 . We prove that if α≠0 then the sub-Riemannian spheres S(0,r) with small radii are not subanalytic.

[ MATH.MATH-OC ] Mathematics [math]/Optimization and Control [math.OC]0209 industrial biotechnologyRiemann manifoldRiemann surface010102 general mathematicsMathematical analysis[MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC]02 engineering and technologyGeneral Medicine01 natural sciencesCombinatoricssymbols.namesake020901 industrial engineering & automationsymbolsOrder (group theory)SPHERES[MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC]0101 mathematicsMathematics
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Minimum Time Control of the Restricted Three-Body Problem

2012

The minimum time control of the circular restricted three-body problem is considered. Controllability is proved on an adequate submanifold. Singularities of the extremal flow are studied by means of a stratification of the switching surface. Properties of homotopy maps in optimal control are framed in a simple case. The analysis is used to perform continuations on the two parameters of the problem: The ratio of the masses, and the magnitude of the control.

[ MATH.MATH-OC ] Mathematics [math]/Optimization and Control [math.OC]Surface (mathematics)0209 industrial biotechnologyControl and OptimizationApplied MathematicsHomotopy010102 general mathematicsMathematical analysis[MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC]02 engineering and technologyThree-body problemOptimal controlSubmanifold01 natural sciencesControllability020901 industrial engineering & automationSimple (abstract algebra)Gravitational singularity[MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC]0101 mathematicsMathematicsSIAM Journal on Control and Optimization
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Moment-angle complexes and complexe manifolds

2010

The aim of this thesis is to extend the results of the article [B-M] on the relations between moment-angle complexes and complex manifolds. We will focus here on moment-angle complexes defined by a simplicial (not only polytopal) decomposition of the sphere. We will also seek to use the relationship between these two kinds of objects to be understand the topology of several complex manifolds. [B-M] F.Bosio, L.Meersseman, Real quadrics in Cn, complex manifolds and polytopes, Acta Mathematica, 197 (2006), n° 1, 53 -- 127.

[MATH.MATH-GM]Mathematics [math]/General Mathematics [math.GM]Complex manifoldsSphères simpliciales[ MATH.MATH-GM ] Mathematics [math]/General Mathematics [math.GM]Complexes moment-angle[MATH.MATH-GM] Mathematics [math]/General Mathematics [math.GM]Moment-angle complexesVariétés complexesSimplicial spheres
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The Role of Differential Parameters in Beltrami's Work

1997

Abstract Differential parameters play a relevant role in Beltrami's mathematical work. They are employed in different contexts, in order to express some well-known results in a new way and to extend potential theory and the theory of elasticity to a Riemannian manifold. The author aims to show that differential parameters enabled Beltrami to solve many mathematical questions and that they constitute the first step toward the conception of tensor calculus. Les parametres differentiels jouent un role important dans l'oeuvre mathematique de Beltrami. Ils sont employes en contextes differents, pour exprimer dans une maniere nouvelle quelques resultats bien-connus et pour generaliser la theorie …

[SHS.HISPHILSO]Humanities and Social Sciences/History Philosophy and Sociology of Sciencesdifferential parameterstensor calculusMathematics(all)HistoryRiemannian manifoldGeneral MathematicsCalculusBeltrami[MATH]Mathematics [math]HumanitiesMathematicsHistoria Mathematica
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