Search results for "Combinatorics"

showing 10 items of 1770 documents

Invariant Jordan curves of Sierpinski carpet rational maps

2015

In this paper, we prove that if $R\colon\widehat{\mathbb{C}}\to\widehat{\mathbb{C}}$ is a postcritically finite rational map with Julia set homeomorphic to the Sierpi\'nski carpet, then there is an integer $n_0$, such that, for any $n\ge n_0$, there exists an $R^n$-invariant Jordan curve $\Gamma$ containing the postcritical set of $R$.

Mathematics::Dynamical SystemsGeneral Mathematics[MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS]rational functionsMathematics::General TopologyDynamical Systems (math.DS)01 natural sciences37F10Combinatoricsexpanding Thusrston mapssymbols.namesakeHigh Energy Physics::TheoryMathematics::Quantum AlgebraFOS: MathematicsMathematics::Metric GeometryMathematics - Dynamical Systems0101 mathematicsInvariant (mathematics)MathematicsmatematiikkamathematicsSierpinski carpet Julia setsApplied Mathematicsta111010102 general mathematicsinvariant Jordan curveJulia setJordan curve theoremrationaalifunktiot010101 applied mathematicsrational mapsSierpinski carpetsymbols
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Multi-layer canard cycles and translated power functions

2008

Abstract The paper deals with two-dimensional slow-fast systems and more specifically with multi-layer canard cycles. These are canard cycles passing through n layers of fast orbits, with n ⩾ 2 . The canard cycles are subject to n generic breaking mechanisms and we study the limit cycles that can be perturbed from the generic canard cycles of codimension n . We prove that this study can be reduced to the investigation of the fixed points of iterated translated power functions.

Mathematics::Dynamical SystemsLiénard equationCanard cycleQuantitative Biology::Neurons and CognitionApplied MathematicsMathematical analysisCodimensionSlow-fast systemFixed pointCombinatoricsIterated functionLiénard equationBifurcationLimit (mathematics)Power functionMulti layerBifurcationAnalysisMathematicsJournal of Differential Equations
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Feuilletages deCP(n) : de l’holonomie hyperbolique pour les minimaux exceptionnels

1992

Let ℱ be a holomorphic foliation ofCP(n). If ℱ has a leaf L, the closure L of which is disjoint from the singular set of the foliation, we prove that there exists a loop in a leaf contained in L with contracting hyperbolic holonomy.

Mathematics::Dynamical SystemsQuantitative Biology::Tissues and OrgansGeneral MathematicsMathematical analysisHolomorphic functionHolonomyClosure (topology)Disjoint setsFoliationCombinatoricsLoop (topology)Mathematics::Differential GeometryMathematics::Symplectic GeometryMathematicsPublications mathématiques de l'IHÉS
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Pseudo-rotations of the closed annulus : variation on a theorem of J. Kwapisz

2003

Consider a homeomorphism h of the closed annulus S^1*[0,1], isotopic to the identity, such that the rotation set of h is reduced to a single irrational number alpha (we say that h is an irrational pseudo-rotation). For every positive integer n, we prove that there exists a simple arc gamma joining one of the boundary component of the annulus to the other one, such that gamma is disjoint from its n first iterates under h. As a corollary, we obtain that the rigid rotation of angle alpha can be approximated by homeomorphisms conjugate to h. The first result stated above is an analog of a theorem of J. Kwapisz dealing with diffeomorphisms of the two-torus; we give some new, purely two-dimension…

Mathematics::Dynamical Systems[MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS][ MATH.MATH-DS ] Mathematics [math]/Dynamical Systems [math.DS]General Physics and AstronomyBoundary (topology)Dynamical Systems (math.DS)Disjoint sets01 natural sciences37E45 37E30CombinatoricsInteger0103 physical sciencesFOS: Mathematics0101 mathematicsMathematics - Dynamical SystemsMathematical PhysicsMathematicsApplied Mathematics010102 general mathematicsStatistical and Nonlinear PhysicsAnnulus (mathematics)TorusMathematics::Geometric TopologyHomeomorphismIterated function010307 mathematical physicsDiffeomorphism
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The variation of the maximal function of a radial function

2017

We study the problem concerning the variation of the Hardy-Littlewood maximal function in higher dimensions. As the main result, we prove that the variation of the non-centered Hardy-Littlewood maximal function of a radial function is comparable to the variation of the function itself.

Mathematics::Functional Analysis42B25 46E35 26A45maximal functionGeneral Mathematicsta111010102 general mathematicsMathematics::Classical Analysis and ODEsradial functionharmoninen analyysi01 natural sciences010101 applied mathematicsCombinatoricsRadial functionMathematics - Classical Analysis and ODEsClassical Analysis and ODEs (math.CA)FOS: Mathematics46E35Maximal operatorMaximal function0101 mathematicsfunktionaalianalyysi42B25Variation (astronomy)26A45MathematicsArkiv för Matematik
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The Bishop–Phelps–Bollobás point property

2016

Abstract In this article, we study a version of the Bishop–Phelps–Bollobas property. We investigate a pair of Banach spaces ( X , Y ) such that every operator from X into Y is approximated by operators which attain their norm at the same point where the original operator almost attains its norm. In this case, we say that such a pair has the Bishop–Phelps–Bollobas point property (BPBpp). We characterize uniform smoothness in terms of BPBpp and we give some examples of pairs ( X , Y ) which have and fail this property. Some stability results are obtained about l 1 and l ∞ sums of Banach spaces and we also study this property for bilinear mappings.

Mathematics::Functional AnalysisApplied Mathematics010102 general mathematicsBanach spaceBilinear interpolationStability resultBilinear form01 natural sciences010101 applied mathematicsCombinatoricsOperator (computer programming)Norm (mathematics)0101 mathematicsBishop–Phelps theoremAnalysisMathematicsJournal of Mathematical Analysis and Applications
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Noncommutative Davis type decompositions and applications

2018

We prove the noncommutative Davis decomposition for the column Hardy space $\H_p^c$ for all $0<p\leq 1$. A new feature of our Davis decomposition is a simultaneous control of $\H_1^c$ and $\H_q^c$ norms for any noncommutative martingale in $\H_1^c \cap \H_q^c$ when $q\geq 2$. As applications, we show that the Burkholder/Rosenthal inequality holds for bounded martingales in a noncommutative symmetric space associated with a function space $E$ that is either an interpolation of the couple $(L_p, L_2)$ for some $1<p<2$ or is an interpolation of the couple $(L_2, L_q)$ for some $2<q<\infty$. We also obtain the corresponding $\Phi$-moment Burkholder/Rosenthal inequality for Orlicz functions that…

Mathematics::Functional AnalysisMathematics::Operator AlgebrasFunction spaceGeneral Mathematics010102 general mathematicsType (model theory)Hardy space01 natural sciencesNoncommutative geometryCombinatorics010104 statistics & probabilitysymbols.namesakeSymmetric spaceBounded functionsymbols0101 mathematicsMartingale (probability theory)MathematicsJournal of the London Mathematical Society
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On the size of the set of unbounded multilinear operators between Banach spaces

2020

Among other results we investigate $\left( \alpha,\beta\right) $-lineability of the set of non-continuous $m$-linear operators defined between normed spaces as a subset of the space of all $m$-linear operators. We also give a partial answer to an open problem on the lineability of the set of non absolutely summing operators.

Mathematics::Functional AnalysisNumerical AnalysisPure mathematicsMultilinear mapAlgebra and Number TheoryOpen problem010102 general mathematicsBanach space010103 numerical & computational mathematicsSpace (mathematics)01 natural sciencesFunctional Analysis (math.FA)Mathematics - Functional AnalysisSet (abstract data type)FOS: MathematicsDiscrete Mathematics and CombinatoricsGeometry and Topology0101 mathematicsMathematicsLinear Algebra and its Applications
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New applications of extremely regular function spaces

2017

Let $L$ be an infinite locally compact Hausdorff topological space. We show that extremely regular subspaces of $C_0(L)$ have very strong diameter $2$ properties and, for every real number $\varepsilon$ with $0<\varepsilon<1$, contain an $\varepsilon$-isometric copy of $c_0$. If $L$ does not contain isolated points they even have the Daugavet property, and thus contain an asymptotically isometric copy of $\ell_1$.

Mathematics::Functional AnalysisProperty (philosophy)Function spaceMathematics::Operator AlgebrasGeneral MathematicsHausdorff spaceTopological spaceLinear subspaceFunctional Analysis (math.FA)CombinatoricsMathematics - Functional AnalysisFOS: Mathematics46B20 46B22Locally compact spaceMathematicsReal number
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Some kind of Bishop-Phelps-Bollobás property

2016

In this paper we introduce two Bishop–Phelps–Bollobas type properties for bounded linear operators between two Banach spaces X and Y: property 1 and property 2. These properties are motivated by a Kim–Lee result which states, under our notation, that a Banach space X is uniformly convex if and only if the pair (X,K) satisfies property 2. Positive results of pairs of Banach spaces (X,Y) satisfying property 1 are given and concrete pairs of Banach spaces (X,Y) failing both properties are exhibited. A complete characterization of property 1 for the pairs (lp,lq) is also provided.

Mathematics::Functional AnalysisPure mathematicsProperty (philosophy)Approximation propertyGeneral Mathematics010102 general mathematicsRegular polygonBanach space010103 numerical & computational mathematicsType (model theory)Characterization (mathematics)01 natural sciencesCombinatoricsBounded function0101 mathematicsBishop–Phelps theoremMathematicsMathematische Nachrichten
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