By Rainer Klages (auth.), Xavier Leoncini, Marc Leonetti (eds.)

ISBN-10: 1461469619

ISBN-13: 9781461469612

ISBN-10: 1461469627

ISBN-13: 9781461469629

*From Hamiltonian Chaos to advanced platforms: A Nonlinear Physics Approach* collects contributions on fresh advancements in non-linear dynamics and statistical physics with an emphasis on complicated platforms. This booklet presents quite a lot of state of the art learn in those fields. The unifying element of this publication is demonstration of ways related instruments coming from dynamical platforms, nonlinear physics, and statistical dynamics can result in a wide landscape of analysis in quite a few fields of physics and past, such a lot particularly with the viewpoint of software in complicated structures.

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63) we have ρ (Wt ) ∼ ρ (x,t). It thus remains to solve Eq. 69) by preserving the FDR1 Eq. 65). Here and in the following we denote ensemble averages in case of a nonzero external field with the subscript F. For Gaussian stochastic processes we have seen in the previous section that the conventional work TFR follows from FDR1. Hence, for the above power-law correlated internal Gaussian noise, we recover the conventional work TFR Eq. 58). 70) which represents a special case of Eq. 66) with a memory kernel modeled by a delta-function.

R. Devaney, An Introduction to Chaotic Dynamical Systems, 2nd edn. (Addison-Wesley, Reading, 1989) 40. M. Thaler, Israel J. Math. 46, 67 (1983) 41. R. Zweim¨uller, Nonlinearity 11, 1263 (1998) 42. N. Korabel, E. Barkai, Phys. Rev. Lett. 102, 050601/1 (2009) 43. N. Korabel, E. Barkai, Phys. Rev. E 82, 016209/1 (2010) 44. M. Thaler, Infinite ergodic theory. htm 45. R. Zweim¨uller, Surrey notes on infinite ergodic theory. pdf 46. P. J. Wang, Proc. Nat. Acad. Sci. USA 85, 4591 (1988) 47. S. Galatolo, Nonlinearity 16, 1219 (2003) 48.

40) which has the following probabilistic meaning: The PDF to find a particle at position x at time t is equal to the PDF to find it at point x at some previous time t multiplied with the transition probability to get from (x ,t ) to (x,t) integrated over all possible values of x and t . The second term accounts for the probability of remaining at the initial position x = 0. 41) 0 where the hat stands for the Fourier transform and the tilde for the Laplace transform. Respectively, this function obeys the Fourier-Laplace transform of 4 In detail, the definition of a generalized diffusion coefficient is a bit more subtle [26].

### From Hamiltonian Chaos to Complex Systems: A Nonlinear Physics Approach by Rainer Klages (auth.), Xavier Leoncini, Marc Leonetti (eds.)

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