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Saturday, August 8, 2020 | History

3 edition of stability theorem for foliations with singularities found in the catalog.

stability theorem for foliations with singularities

Andrzej PiaМЁtkowski

stability theorem for foliations with singularities

by Andrzej PiaМЁtkowski

  • 272 Want to read
  • 20 Currently reading

Published by Państwowe Wydawn. Nauk. in Warszawa .
Written in English

    Subjects:
  • Foliations (Mathematics),
  • Singularities (Mathematics)

  • Edition Notes

    Bibliography: p. [48]-49.

    StatementAndrzej Piątkowski.
    SeriesDissertationes mathematicae = Rozprawy matematyczne,, 267, Rozprawy matematyczne ;, 267.
    Classifications
    LC ClassificationsQA1 .D54 no. 267, QA613.62 .D54 no. 267
    The Physical Object
    Pagination52 p. :
    Number of Pages52
    ID Numbers
    Open LibraryOL2255022M
    ISBN 108301081163
    LC Control Number89133210

    Dynamical Systems is a collection of papers that deals with the generic theory of dynamical systems, in which structural stability becomes associated with a generic property. Some papers describe structural stability in terms of mappings of one manifold into another, as well as their singularities. CHAPTER 9. ISOLATED SINGULARITIES AND THE RESIDUE THEOREM 94 Example The function exp 1 z does not have a removable singularity (consider, for example, lim x!0+ exp 1 x = 1). On the other hand, exp 1 z approaches 0 as z approaches 0 from the negative real axis. Hence lim z!0 exp 1 z 6= 1, that is, exp 1 z has an essential singularity at 0.

    Nonaccumulation theorem for hyperbolic polycycles Chapter V. Global properties of complex polynomial foliations Algebraic leaves of polynomial foliations on the complex projective plane P2 Appendix: Foliations with invariant lines and algebraic leaves of foliations from the class A . on an -dimensional manifold. A decomposition of into path-connected subsets, called leaves, such that can be covered by coordinate neighbourhoods with local coordinates, in terms of which the local leaves, that is, the connected components of the intersection of the leaves with, are given by the equations.A foliation in this sense is called a topological foliation.

    MONGE-AMPERE FOLIATIONS WITH SINGULARITIES AT THE BOUNDARY OF STRONGLY` CONVEX DOMAINS FILIPPO BRACCI AND GIORGIO PATRIZIO Using the work of Chang, Hu and Lee [10], in Theorem , we show that () has a smooth solution on D such and refer to the book [1] for proofs. Also, we state and prove a corollary of the Julia-Wolff-Carath. Introduction to the Geometry of Foliations, Part A by Gilbert Hector, , available at Book Depository with free delivery worldwide.


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Stability theorem for foliations with singularities by Andrzej PiaМЁtkowski Download PDF EPUB FB2

Aim in this paper is to present a variant of a fundamental result in [9], a version of Reeb complete stability theorem for foliations with singularities.

Throughout this paper M will be a connected manifold of dimension m 2 and F a codimension one smooth foliation. Our main result is the following stability theorem: Theorem 1. Let F be a transversally orientable codimension one foliation with Bott–Morse singularities all of center type on a compact connected manifold M.

Assume that F has some compact leaf L with H 1 (L;R) = 0 or there is a codimension greaterorequalslant3 component N ⊂ sing(F) with H 1 (N;R) = : A. Mafra, B. Scárdua. The use of the Reeb Stability theorem in place of the Poincaré–Bendixson theorem paves the way to a three-dimensional version, for foliations with singularities of Morse type, of a classical.

Camacho C. () Structural stability of foliations with singularities. In: Schweitzer P.A. (eds) Differential Topology, Foliations and Gelfand-Fuks Cohomology. Lecture Notes in Mathematics, vol Cited by: 1. [Th] W. Thurston, A generalization of the Reeb Stability Theorem, Topology 13 (), [V] E.

Vogt, Foliations of codimension 2 with all leaves compact, Manuscripta Math. 18 (), STABILITY OF FOLIATIONS While this paper only deals with the stability of foliations in the neighborhood of a given compact leaf, i.e.

stability in J x, Hirsch [HirschJ has dealt with the persistence of the compact leaf under perturbations. Foliation germs at a compact manifold X; the basic homeomorphism theorem. Theorem (Wagneur) [Wag] The one-formω ∈ σ is structurally stable, if and only if the index of 0 ∈ Sing(ω) is neither 2 nor n −2.

Let us denote by S the space of foliations defined by non degenerate one-forms with singularities, whose index is neither 2 nor n −2. Singularities in Foliations (Distributions) Defined by Normal Curvature Properties J. Sotomayor Instituto de Matema´tica e Estat´ıstica Universidade de Sa˜o Paulo [email protected] Work in collaboration with R.

Garcia (UFG) and D. Lopes da Silva. ural stability of foliations with singularities. Differential Topol-ogy, Foliations and Gelfand-Fuks Cohomology Lecture Notes in Math-ematics.

Springer Verlag pp 43–51, ural stability of integrable 1-forms on 3-manifolds. Topology, vol. 17, n 2, pp –, Cr structural stability of germs of integrable 1. iger’s argument to this situation, using strongly the stability theorem of Reeb, as a substitute for the Poincar e-Bendixson arguments.

Along the same line of reasoning we present in x 6 a generalization of Novikov’s compact leaf theorem for the case of foliations with Morse singularities. SPECIALNESS AND ISOTRIVIALITY FOR REGULAR ALGEBRAIC FOLIATIONS EKATERINA AMERIK AND FRÉDÉRIC CAMPANA A Jean-Pierre Demailly Contents 1.

Introduction 2 2. Regular Algebraic Foliations. Compactification. 3 3. The Log-conormal sheaf of F. 4 4. Specialness 5 5. Isotriviality criterion 6 6. Viehweg-Zuo sheaves 6 7. Reeb Stability Theorem 7 8. The use of the Reeb Stability theorem in place of the Poincaré–Bendixson theorem paves the way to a three-dimensional version, for foliations with singularities of Morse type, of a.

Get this from a library. A stability theorem for foliations with singularities. [Andrzej Piątkowski]. Singularities and Foliations. Geometry, Topology and Applications BMMS 2/NBMS 3, Salvador, Brazil, Editors Surveys Papers on Advances in Foliations and Singularity Theory: Topology Geometry and Applications.

Front Matter. This proceedings book brings selected works from two conferences, the 2nd Brazil-Mexico Meeting on Singularity.

We prove a global stability theorem for transversely holomorphic foliations of complex codimension one: if there exists a compact leaf with finite holonomy, then the foliation is a Seifert.

Differential Topology, Foliations and Gelfand-Fuks Cohomology Structural stability of foliations with singularities. Pages Camacho, César. Preview. Un theoreme de Thurston etabli au moyen de l'analyse non standard.

Foliations and Gelfand-Fuks Cohomology Book Subtitle. He did his PhD at the University of São Paulo (), with studies at the University of Liverpool, England. His current research is focused on Singularity and Catastrophe Theory, more specifically on singularities of differential applications; singularities, dynamical systems and geometry; and topology of singular manifolds.

Foliations and the geometry of 3-manifolds This book gives an exposition of the so-called "pseudo-Anosov" theory of foliations of 3-manifolds, generalizing Thurston's theory of surface automorphisms.

A central idea is that of a universal circle for taut foliations and other dynamical objects. CiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): The interplay between the topology of a closed manifold and the combinatorics of the critical points of a real valued function of class C 2 defined on the manifold is a well known fact of Morse Theory.

It is natural to expect a similar relationship for foliated manifolds. A closed, connected oriented three-manifold supporting a codimension one oriented smooth foliation with Morse singularities having more centers than s Cited by: 9. CiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): We study codimension one foliations with singularities defined locally by Bott-Morse functions on closed oriented manifolds.

We carry to this setting the classical concepts of holonomy of invariant sets and stability, and prove a stability theorem in the spirit of the local stability theorem of Reeb.o; Invariant sets near singularities of holomorphic foliations.

Ergodic Theory & Dynamical Systems (Print), v. 36, p.There are many other ways how foliations with Bott-Morse singularities arise.

We show how the classical theory for non-singular foliations, such as Reeb’s stability theorems, extends to singular foliations of this type. In the particular case when all the singularities are transversally centers, our stability theorem yields to a topological.