Hamiltonian Round-Off

  • John H. Lowenstein


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
$$ \psi \left( x \right) = C \cdot x, $$
$$ C = \left( {\begin{array}{*{20}c} \lambda & { - 1} \\ 1 & 0 \\ \end{array} } \right), $$
and λ = 2cos(2πρ) is a quadratic irrational and the rotation number ρ is assumed to be rational.


Periodic Orbit Convex Polygon Rotation Number Symbolic Dynamic Substitution Rule 
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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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