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Tytuł książki

A stability theorem for foliations with singularities

Autorzy

Andrzej Piątkowski

Seria

Rozprawy Matematyczne tom/nr w serii: 267 wydano: 1988

Zawartość

Pełne teksty:
rm26701.pdf

Warianty tytułu

Abstrakty

EN

CONTENTS
Introduction...........................................................................................5
1. Preliminaries.....................................................................................6
2. Chains along a curve......................................................................14
3. Some topological properties of foliations with singularities..............22
4. Holonomy group of a leaf................................................................23
5. A stability theorem...........................................................................34
6. The case of foliations without singularities......................................44
References.........................................................................................48

Słowa kluczowe

Tematy

Wydawca

Instytut Matematyczny Polskiej Akademii Nauk

Miejsce publikacji

Warszawa

Copyright

Seria

Rozprawy Matematyczne tom/nr w serii: 267

Liczba stron

49

Liczba rozdzia³ów

Opis fizyczny

Dissertationes Mathematicae, Tom CCLXVII

Daty

wydano
1988

Twórcy

autor
Andrzej Piątkowski
  • Institute of Mathematics, University of Łódź, Banacha 22, 90-238 Łódź, Poland

Bibliografia

  • [B] R. Bott, Lectures on characteristic classes and foliations, in: Lectures on Algebraic and Differential Topology, Lecture Notes in Math. 279, Springer-Verlag, Berlin 1972, 1-94.
  • [EMS] R. Edwards, K. C. Millett and D. Sullivan, Foliations with all leaves compact, Topology 16 (1977), 13-32.
  • [ER] C. Ehresmann et G. Reeb, Sur les champs d'éléments de contact de dimension p complètement intégrables dans une variété continûment différentiable, C. R. Acad. Sci. Paris 218 (1944), 955-957.
  • [E1] D. B. A. Epstein, Foliations with all leaves compact, Ann. Inst. Fourier 26 (1976), 265-282.
  • [E2] D. B. A. Epstein, Periodic flows on three-manifolds, Ann. of Math. 95 (1972), 66-82.
  • [EV] D. B. A. Epstein and E. Vogt, A counterexample to the Periodic Orbit Conjecture in codimension 3, Ann. of Math. 108 (1978), 539- 552.
  • [H] A. Haefliger, Sur les classes caractéristiques des feuilletages, Séminaire Bourbaki, 1971-1972, no. 412.
  • [HH] G. Hector and U. Hirsch, Introduction to the Geometry of Foliations, Aspects of Math, Vieweg, Braunschweig/Wiesbaden 1981.
  • [He] R. Hermann, On the accessibility problem in control theory, in: Internat. Symp. on Nonlinear Differential Equations and Nonlinear Mechanics, Academic Press, New York 1963, 325-332.
  • [Hi] M. W. Hirsch, Differential Topology, Springer-Verlag, Berlin 1976.
  • [KT] F. W. Kamber and P. Tondeur, Foliated Bundles and Characteristic Classes, Lecture Notes in Math. 493, Springer-Verlag, Berlin 1975.
  • [KN] S. Kobayashi and K. Nomizu, Foundations of Differential Geometry, Volume I, Interscience Tracts Pure Appl. Math. 15, Interscience, New York 1963.
  • [L1] H. B. Lawson, Foliations, Bull. Amer. Math. Soc. 80 (1974), 369-418.
  • [L2] H. B. Lawson, The quantitative theory of foliations, Amer. Math. Soc. Regional Conf., Ser. in Math, 27, 1977.
  • [Lo] C. Lobry, Controllabilité de systèmes non linéaires, SIAM J. Control 8 (1970), 573-605.
  • [N] T. Nagano, Linear differential systems with singularities and application to transitive Lie algebras, J. Math. Soc. Japan 18 (1966), 398-104.
  • [R] G. Recb, Sur certaines propriétés topologiques des variétés feuilletées, Actualités Sci. Indust. 1183, Hermann, Paris 1952.
  • [Rh] B. L. Reinhart, Differential Geometry of Foliations, Springer-Verlag, Berlin 1983.
  • [S1] P. Stefan, Accessibility and foliations with singularities, Bull. Amer. Math. Soc. 80 (1974), 1142-1145.
  • [S2] P. Stefan, Accessible sets, orbits, and foliations with singularities, Proc. London Math. Soc. 29 (1974), 699-713.
  • [S3] P. Stefan, Attainable sets are manifolds, duplicated notes, University College of North Wales, Bangor, June 1973.
  • [Sl1] D. Sullivan, A new flow. Bull. Amer. Math. Soc. 82 (1976), 331-332.
  • [Sl2] D. Sullivan, A counterexample to the periodic orbit conjecture, Publ. IHES 46 (1976), 5-14.
  • [Sul] H. J. Sussmann, Orbits of families of vector fields and integrability of distributions, Trans. Amer. Math. Soc. 180 (1973), 171-188.
  • [Su2] Orbits of families of vector fields and integrability of systems with singularities, Bull. Amer. Math. Soc. 79 (1973), 197-199.
  • [SuJ] H. J. Sussmann and V. Jurdjevic, Controllability of nonlinear systems, J. Differential Equations 12 (1972), 95-116.
  • [T] I. Tamura, Topology of Foliations, "Mir", Moscow 1979 (in Russian, trans), from Japanese).
  • [Th] W. P. Thurston, A generalization of the Reeb Stability Theorem, Topology 13 (1974), 347-352.
  • [V] E. Vogt, Foliations of codimension 2 with all leaves compact, Manuscripta Math. 18 (1976), 187-212.

Języki publikacji

EN

Uwagi

Identyfikator YADDA

bwmeta1.element.zamlynska-731f685a-cfce-46ab-876d-032679e4e175

Identyfikatory

ISBN
83-01-08116-3
ISSN
0012-3862

Kolekcja

DML-PL
Zawartość książki

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