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- Title
Accelerating Cycle Expansions by Dynamical Conjugacy.
- Authors
Gao, Ang; Xie, Jianbo; Lan, Yueheng
- 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.
- Subjects
COMBINATORIAL dynamics; CONJUGACY classes; NONLINEAR systems; EXPONENTIAL functions; STATISTICAL physics
- Publication
Journal of Statistical Physics, 2012, Vol 146, Issue 1, p56
- ISSN
0022-4715
- Publication type
Article
- DOI
10.1007/s10955-011-0369-6