The European Physical Journal Special Topics

, Volume 225, Issue 6–7, pp 1053–1070 | Cite as

Analytical study of chaos and applications

  • G. Contopoulos
  • M. Harsoula
  • C. Efthymiopoulos
Regular Article Session B: Papers I
Part of the following topical collections:
  1. Mathematical Modeling of Complex Systems


We summarize various cases where chaotic orbits can be described analytically. First we consider the case of a magnetic bottle where we have non-resonant and resonant ordered and chaotic orbits. In the sequence we consider the hyperbolic Hénon map, where chaos appears mainly around the origin, which is an unstable periodic orbit. In this case the chaotic orbits around the origin are represented by analytic series (Moser series). We find the domain of convergence of these Moser series and of similar series around other unstable periodic orbits. The asymptotic manifolds from the various unstable periodic orbits intersect at homoclinic and heteroclinic orbits that are given analytically. Then we consider some Hamiltonian systems and we find their homoclinic orbits by using a new method of analytic prolongation. An application of astronomical interest is the domain of convergence of the analytical series that determine the spiral structure of barred-spiral galaxies.


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Copyright information

© EDP Sciences and Springer 2016

Authors and Affiliations

  • G. Contopoulos
    • 1
  • M. Harsoula
    • 1
  • C. Efthymiopoulos
    • 1
  1. 1.Research Center for Astronomy and Applied Mathematics of the Academy of AthensAthensGreece

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