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Journal of Statistical Physics

, Volume 146, Issue 1, pp 56–66 | Cite as

Accelerating Cycle Expansions by Dynamical Conjugacy

  • Ang Gao
  • Jianbo Xie
  • Yueheng Lan
Article
  • 68 Downloads

Abstract

Periodic orbit theory provides two important functions—the dynamical zeta function and the spectral determinant for the calculation of dynamical averages in a nonlinear system. Their cycle expansions converge rapidly when the system is uniformly hyperbolic but greatly slow down in the presence of non-hyperbolicity. We find that the slow convergence can be attributed to singularities in the natural measure. A properly designed coordinate transformation may remove these singularities and results in a dynamically conjugate system where fast convergence is restored. The technique is successfully demonstrated on several examples of one-dimensional maps and some remaining challenges are discussed.

Keywords

Cycle expansions Periodic orbit theory Nonlinear dynamics Nonequilibrium statistical physics Dynamical zeta function 

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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.The Department of PhysicsTsinghua UniversityBeijingChina
  2. 2.The Department of PhysicsUC BerkeleyBerkeleyUSA

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