Bifurcations of Periodic Orbits

  • Kenneth R. Meyer
  • Glen R. Hall
Part of the Applied Mathematical Sciences book series (AMS, volume 90)


This chapter and Chapter IX use the theory of normal forms developed in Chapter VI. They contain an introduction to generic bifurcation theory and its applications. Bifurcation theory has grown into a vast subject with a large literature; so, this chapter can only present the basics of the theory. The primary focus of this chapter is the study of periodic solutions—their existence and evolution. Periodic solutions abound in Hamiltonian systems. In fact, a famous Poincaré conjecture is that periodic solutions are dense in a generic Hamiltonian system, a point that was established in the C 1 case by Pugh and Robinson (1977).


Periodic Solution Periodic Orbit Normal Form Periodic Point Implicit Function Theorem 
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Copyright information

© Springer Science+Business Media New York 1992

Authors and Affiliations

  • Kenneth R. Meyer
    • 1
  • Glen R. Hall
    • 2
  1. 1.Department of Mathematical SciencesUniversity of CincinnatiCincinnatiUSA
  2. 2.Mathematics DepartmentBoston UniversityBostonUSA

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