TY - JOUR

T1 - Diffusion coefficient of piecewise linear maps

AU - Chen, Chia Chu

N1 - Copyright:
Copyright 2015 Elsevier B.V., All rights reserved.

PY - 1995

Y1 - 1995

N2 - By using the cycle expansion, we obtain general expressions for the determination of the diffusion coefficient D of a piecewise linear map which is parametrized by k and h (where the map contains 2k+5 branches of line segment, and h is the height of the shortest line). By restricting h=β/m [β=1,...,(k+1)/2; m is the slope of the map], a closed form expression of D can be obtained and some of its consequences are discussed. The limiting form of D (k→) is then shown to be k2. For the simplest case with k=1, we also show that more exact results can be found. A limiting case with h→0 is discussed where agreement with the result obtained from the invariant measure approach is established.

AB - By using the cycle expansion, we obtain general expressions for the determination of the diffusion coefficient D of a piecewise linear map which is parametrized by k and h (where the map contains 2k+5 branches of line segment, and h is the height of the shortest line). By restricting h=β/m [β=1,...,(k+1)/2; m is the slope of the map], a closed form expression of D can be obtained and some of its consequences are discussed. The limiting form of D (k→) is then shown to be k2. For the simplest case with k=1, we also show that more exact results can be found. A limiting case with h→0 is discussed where agreement with the result obtained from the invariant measure approach is established.

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U2 - 10.1103/PhysRevE.51.2815

DO - 10.1103/PhysRevE.51.2815

M3 - Article

AN - SCOPUS:0000530282

VL - 51

SP - 2815

EP - 2822

JO - Physical review. E

JF - Physical review. E

SN - 1539-3755

IS - 4

ER -