Abstract
In this lecture we consider the influence of weak stochastic perturbations on period doubling using nonequilibrium potentials, a concept which is explained in section 1 and formulated for the case of maps in section 2. In section 3 nonequilibrium potentials are considered for the family of quadratic maps (a) at the Feigenbaum ‘attractor’ with Gaussian noise, (b) for more general non-Gaussian noise, and (c) for the case of a strange repeller. Our discussion will be informal. A more detailed account of this and related material can be found in our papers [1-3] and in the reviews [4, 5], where further references to related work are also given.
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References
R. Graham, A. Hamm and T. Tel, Phys. Rev. Lett. 66, 3089 (1991).
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A. Hamm and R. Graham, ‘Scaling for Small Random Perturbations of Golden Critical Circle Maps’, preprint (Essen, 1992).
R. Graham and A. Hamm, in From Phase Transitions to Chaos eds. G. Györgyi, I. Kondor, L. Sasvári, and T. Tel, (World Scientific, Singapore 1992).
R. Graham and A. Hamm, in Evolution of Dynamical Structures in Complex Systems eds. A. Wunderlin and R. Friedrich, (Springer, Berlin 1992).
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© 1993 Springer Science+Business Media Dordrecht
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Graham, R., Hamm, A. (1993). Nonequilibrium Potentials For Period Doubling. In: Tirapegui, E., Zeller, W. (eds) Instabilities and Nonequilibrium Structures IV. Mathematics and Its Applications, vol 267. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-1906-1_1
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DOI: https://doi.org/10.1007/978-94-011-1906-1_1
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