Journal
JOURNAL OF STATISTICAL PHYSICS
Volume 146, Issue 1, Pages 56-66Publisher
SPRINGER
DOI: 10.1007/s10955-011-0369-6
Keywords
Cycle expansions; Periodic orbit theory; Nonlinear dynamics; Nonequilibrium statistical physics; Dynamical zeta function
Categories
Funding
- National Natural Science Foundation of China [10975081]
- Ph.D. Program Foundation of Ministry of Education of China [20090002120054]
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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.
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