Onset of Dynamical Chaos: Mathematical Aspects

  • Sadrilla AbdullaevEmail author
Part of the Springer Series on Atomic, Optical, and Plasma Physics book series (SSAOPP, volume 78)


The theory of chaos originated in the works by H. Poincaré is related to the problem of integrability of Hamiltonian systems under small periodic perturbations, i.e., to the fundamental problem of dynamics (see, Sect.  6.2.1). Chaos of magnetic field lines in magnetic fusion devices is an excellent example of dynamical chaos in Hamiltonian systems with one-and-half-degrees of freedom. In this chapter we discuss the some mathematical aspects of the onset of chaos in Hamiltonian systems.


Periodic Orbit Hamiltonian System Lyapunov Exponent Unstable Manifold Magnetic Surface 
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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.Institute of Energy and Climate ResearchForschungszentrum JülichJülichGermany

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