Nonlinear Sciences – Chaotic Dynamics
Scientific paper
2001-01-19
Nonlinear Sciences
Chaotic Dynamics
Uses REVTEX; to be published in Phys. Rev. Lett
Scientific paper
10.1103/PhysRevLett.86.2778
We present a novel method for the calculation of the fractal dimension of boundaries in dynamical systems, which is in many cases many orders of magnitude more efficient than the uncertainty method. We call it the Output Function Evaluation (OFE) method. The OFE method is based on an efficient scheme for computing output functions, such as the escape time, on a one-dimensional portion of the phase space. We show analytically that the OFE method is much more efficient than the uncertainty method for boundaries with $D<0.5$, where $D$ is the dimension of the intersection of the boundary with a one-dimensional manifold. We apply the OFE method to a scattering system, and compare it to the uncertainty method. We use the OFE method to study the behavior of the fractal dimension as the system's dynamics undergoes a topological transition.
de Moura Alessandro P. S.
Grebogi Celso
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