Hamiltonian Round-Off

  • John H. Lowenstein

Abstract

In this final chapter, we shift our attention to a variation on the theme of a resonantly kicked one-dimensional harmonic oscillator, namely a model of an invertible, area-preserving round-off map (Vivaldi, 1994; Lowenstein et al., 1997; Lowenstein and Vivaldi, 1998, 2000; Lowenstein and Liu, 2003; Akiyama et al., 2008). Here the oscillator is represented stroboscopically by application of the generalized rotation
$$ \psi \left( x \right) = C \cdot x, $$
where
$$ C = \left( {\begin{array}{*{20}c} \lambda & { - 1} \\ 1 & 0 \\ \end{array} } \right), $$
and λ = 2cos(2πρ) is a quadratic irrational and the rotation number ρ is assumed to be rational.

Keywords

Periodic Orbit Convex Polygon Rotation Number Symbolic Dynamic Substitution Rule 
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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References

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Copyright information

© Higher Education Press, Beijing and Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • John H. Lowenstein
    • 1
  1. 1.Department of PhysicsNew York UniversityNew YorkUSA

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