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Dynamical Systems

  • Stavros C. Farantos
Chapter
Part of the SpringerBriefs in Molecular Science book series (BRIEFSMOLECULAR)

Abstract

The basic theory of dynamical systems is introduced in this chapter. Invariant phase space structures—equilibria, periodic orbits, tori, normally hyperbolic invariant manifolds and stable/unstable manifolds—are defined mainly with graphs produced by numerically solving the equations of motion of 1, 2 and 3 degrees of freedom model Hamiltonian systems. Stability analysis and elementary bifurcations of equilibria and periodic orbits are discussed. The center-saddle, pitchfork, period doubling and complex instability elementary bifurcations encountered in continuation diagrams of equilibria and periodic orbits by varying a parameter in the potential function or the energy of the system are investigated. Methods of analysing non-periodic orbits, regular and chaotic, such as Poincaré surfaces of section, maximal Lyapunov exponent and autocorrelation functions are introduced and explained.

Keywords

Periodic Orbit Unstable Manifold Fundamental Matrix Monodromy Matrix Maximal Lyapunov Exponent 
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.

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Copyright information

© The Author(s) 2014

Authors and Affiliations

  1. 1.Department of ChemistryUniversity of CreteIraklionGreece
  2. 2.Institute of Electronic Structure and LaserFoundation for Research and Technology-HellasIraklionGreece

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