In this chapter, we recall some known mathematical notations, notions and results which will be used later to help readers to understand this book better. For more details, we refer readers to quoted textbooks of nonlinear functional analysis, differential topology, singularities of smooth maps, complex analysis and dynamical systems.


Banach Space Vector Bundle Implicit Function Theorem Multivalued Mapping Exponential Dichotomy 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    K. DEIMLING: Nonlinear Functional Analysis, Springer, Berlin, 1985.zbMATHCrossRefGoogle Scholar
  2. 2.
    W. RUDIN: Real and Complex Analysis, McGraw-Hill, Inc., New York, 1974.zbMATHGoogle Scholar
  3. 3.
    K. YOSIDA: Functional Analysis, Springer-Verlag, Berlin, 1965.zbMATHGoogle Scholar
  4. 4.
    M.S. BERGER: Nonlinearity and Functional Analysis, Academic Press, New York, 1977.zbMATHGoogle Scholar
  5. 5.
    S.N. CHOW & J.K. HALE: Methods of Bifurcation Theory, Springer, New York, 1982.zbMATHCrossRefGoogle Scholar
  6. 6.
    S.G. KRANTZ & H.R. PARKS: The Implicit Function Theorem, History, Theory, and Applications, Birkhäuser, Boston, 2003.CrossRefGoogle Scholar
  7. 7.
    M. FEČKAN: Note on a local invertibility, Math. Slovaca 46 (1996), 285–289.MathSciNetzbMATHGoogle Scholar
  8. 8.
    J. ANDRES & L. GÓRNIEWICZ: Topological Fixed Point Principles for Boundary Value Problems, Kluwer Academic Publishers, Dordrecht, 2003.zbMATHCrossRefGoogle Scholar
  9. 9.
    L. GÓRNIEWICZ: Topological Fixed Point Theory for Multivalued Mappings, Kluwer Academic Publishers, Dordrecht, 1999.Google Scholar
  10. 10.
    A. ORNELAS: Parametrization of Carathéodory multifunctions, Rend. Sem. Mat. Univ. Padova 83 (1990), 33–44.MathSciNetzbMATHGoogle Scholar
  11. 11.
    R. ABRAHAM, J.E. MARSDEN & T. RATIU: Manifolds, Tensor Analysis and Applications, Addison-Wesley, Reading MA, 1983.zbMATHGoogle Scholar
  12. 12.
    M.W. HIRSCH: Differential Topology, Springer-Verlag, New York, 1976.zbMATHCrossRefGoogle Scholar
  13. 13.
    J.P. PALIS & W. DE MELO: Geometric Theory of Dynamical Systems: An Introduction, Springer-Verlag, New York, 1982.zbMATHCrossRefGoogle Scholar
  14. 14.
    M. GOLUBITSKY & V. GUILLEMIN: Stable Mappings and their Singularities, Springer-Verlag, New York, 1973.zbMATHCrossRefGoogle Scholar
  15. 15.
    K.J. PALMER: Shadowing in Dynamical Systems, Theory and Applications, Kluwer Academic Publishers, Dordrecht, 2000.zbMATHCrossRefGoogle Scholar
  16. 16.
    M.C. IRWIN: Smooth Dynamical Systems, Academic Press, London, 1980.zbMATHGoogle Scholar
  17. 17.
    K.J. PALMER: Exponential dichotomies, the shadowing lemma and transversal homoclinic points, Dynamics Reported 1 (1988), 265–306.MathSciNetCrossRefGoogle Scholar
  18. 18.
    R. DEVANEY: An Introduction to Chaotic Dynamical Systems, Benjamin/Cummings, Menlo Park, CA, 1986.zbMATHGoogle Scholar
  19. 19.
    S. WIGGINS: Chaotic Transport in Dynamical Systems, Springer-Verlag, New York, 1992.zbMATHCrossRefGoogle Scholar
  20. 20.
    P. HARTMAN: Ordinary Differential Equations, JohnWiley & Sons, Inc., New York, 1964.zbMATHGoogle Scholar
  21. 21.
    J. K. HALE: Ordinary Differential Equations, 2nd ed., Robert E. Krieger, New York, 1980.zbMATHGoogle Scholar
  22. 22.
    J.L. DALECKII & M.G. KREIN: Stability of Differential Equations, Nauka, Moscow, 1970, (in Russian).Google Scholar
  23. 23.
    K.J. PALMER: Exponential dichotomies and transversal homoclinic points, J. Differential Equations 55 (1984), 225–256.MathSciNetzbMATHCrossRefGoogle Scholar
  24. 24.
    J. GUCKENHEIMER & P. HOLMES: Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields, Springer, New York, 1983.zbMATHGoogle Scholar
  25. 25.
    F. BATTELLI & M. FEČKAN: Global center manifolds in singular systems, NoDEA: Nonl. Diff. Eq. Appl. 3 (1996), 19–34.CrossRefGoogle Scholar
  26. 26.
    J.A. SANDERS, F. VERHULST & J. MURDOCK: Averaging Methods in Nonlinear Dynamical Systems, 2nd ed., Springer, 2007.Google Scholar
  27. 27.
    B. AULBACH & T. WANNER: The Hartman-Grobman theorem for Carathéodory-type differential equations in Banach space, Nonl. Anal., Th. Meth. Appl. 40 (2000), 91–104.MathSciNetzbMATHCrossRefGoogle Scholar
  28. 28.
    B. AULBACH & T. WANNER: Integral manifolds for Carathéodory-type differential equations in Banach space, in: “Six Lectures on Dynamical Systems”, B. Aulbach, F. Colonius, Eds., World Scientific, Singapore, 1996, 45–119.CrossRefGoogle Scholar

Copyright information

© Higher Education Press, Beijing and Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Michal Fečkan
    • 1
  1. 1.Department of Mathematical Analysis and Numerical Mathematics Faculty of Mathematics, Physics and InformaticsComenius University Mlynská dolinaBratislavaSlovakia

Personalised recommendations