Accelerating Cycle Expansions by Dynamical Conjugacy

作者：Gao Ang; Xie Jianbo; Lan Yueheng^*

来源：Journal of Statistical Physics, 2012, 146(1): 56-66.

DOI：10.1007/s10955-011-0369-6

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

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.

• 出版日期2012-1
• 单位清华大学