Nonlinear Sciences – Chaotic Dynamics
Scientific paper
1997-11-27
Phys. Rev. E 57, 5303 (1998)
Nonlinear Sciences
Chaotic Dynamics
8 pages, revtex with 8 embedded postscript figures
Scientific paper
10.1103/PhysRevE.57.5303
We compute the diffusion coefficient and the Lyapunov exponent for a diffusive intermittent map by means of cycle expansion of dynamical zeta functions. The asymptotic power law decay of the coefficients of the relevant power series are known analytically. This information is used to resum these power series into generalized power series around the algebraic branch point whose immediate vicinity determines the desired quantities. In particular we consider a realistic situation where all orbits with instability up to a certain cutoff are known. This implies that only a few of the power series coefficients are known exactly and a lot of them are only approximately given. We develop methods to extract information from these stability ordered cycle expansions and compute accurate values for the diffusion coefficient and the Lyapunov exponent. The method works successfully all the way up to a phase transition of the map, beyond which the diffusion coefficient and Lyapunov exponent are both zero.
Dahlqvist Per
Dettmann Carl P.
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