Showing papers by "Jean-Pierre Eckmann published in 1986"
TL;DR: An algorithm for computing Liapunov exponents from an experimental time series is analyzed and a hydrodynamic experiment is investigated.
Abstract: We analyze in detail an algorithm for computing Liapunov exponents from an experimental time series. As an application, a hydrodynamic experiment is investigated.
860 citations
TL;DR: The basic scaling behavior in both cases is shown to be rooted in the thermodynamic formalism of dynamical systems, stressing their use in characterizing complex behavior.
Abstract: Due to fluctuations around the metric entropy of chaotic dynamical systems there exists a spectrum of invariant dynamical scaling indices, complementary to the range of invariant static scaling indices which have been discovered and applied recently. The basic scaling behavior in both cases is shown to be rooted in the thermodynamic formalism of dynamical systems. An explicit simple example of these ideas is given, stressing their use in characterizing complex behavior.
151 citations
TL;DR: In this article, the authors study a fourth order semilinear parabolic equation on the infinite real line and show that in a certain parameter range, this equation has propagating front solutions (solutions tending to 0 at +∞ and advancing to the right with a speedc) which leave behind them aperiodic pattern in the laboratory frame.
Abstract: In this paper, we study a fourth order semilinear parabolic equation on the infinite real line. We show that in a certain parameter range, this equation has propagating front solutions (solutions tending to 0 at +∞ and advancing to the right with a speedc) which leave behind them aperiodic pattern in the laboratory frame. This is thus an example of spontaneous pattern formation.
39 citations
TL;DR: In the theory of circle maps with golden ratio rotation number formulated by Feigenbaum, Kadanoff, and Shenker as mentioned in this paper, a central role is played by fixed points of a certain composition operator in map space.
Abstract: In the theory of circle maps with golden ratio rotation number formulated by Feigenbaum, Kadanoff, and Shenker [FKS], and by Ostlund, Rand, Sethna, and Siggia [ORSS], a central role is played by fixed points of a certain composition operator in map space. We define a common setting for the problem of proving the existence of these fixed points and of those occurring in the theory of maps of the interval. We give a proof of the existence of the fixed points for a wide range of the parameters on which they depend.
31 citations
TL;DR: In this article, the authors studied a fourth order semilinear parabolic equation on the infinite real line and showed that in a certain parameter range, this equation has propagating front solutions (solutions tending to 0 at + ∞ and advancing to the right with a speed c ) which leave behind them a periodic pattern in the laboratory frame.
Abstract: In this paper, we study a fourth order semilinear parabolic equation on the infinite real line. We show that in a certain parameter range, this equation has propagating front solutions (solutions tending to 0 at + ∞ and advancing to the right with a speed c ) which leave behind them a periodic pattern in the laboratory frame. This is thus an example of spontaneous pattern formation.
1 citations
Duke University1, University of Geneva2, Courant Institute of Mathematical Sciences3, University of California, Los Angeles4, Northeastern University5, Institut des Hautes Études Scientifiques6, Rutgers University7, University of Chicago8, New York University9, University of Rome Tor Vergata10, Sapienza University of Rome11, Ludwig Maximilian University of Munich12