Linear and nonlinear response of discrete dynamical systems |
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Authors: | J. Heldstab H. Thomas T. Geisel G. Radons |
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Affiliation: | 1. Institut für Theoretische Physik der Universit?t, Klingelbergstrasse 82, CH-4056, Basel, Switzerland 2. Institut für Theoretische Physik der Universit?t, Universit?tsstrasse 31, D-8400, Regensburg, Federal Republic of Germany
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Abstract: | We carry out a linear response theory for discrete dynanmical systems with periodic attractors. The symmetry properties of the susceptibility matrix are studied and its eigenvalues and eigenvectors are determined. Close to a period-doubling bifurcation where the susceptibility diverges, its half-width is related to the Lyapunov exponent. At the transition to chaos the susceptibility has some universal behaviour which is described by a critical exponent κ=1?(ln2/lnδ)=0.550193... At the bifurcation points where linear response theory becomes insufficient we also determine the nonlinear response. |
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