ar X iv : c ha o - dy n / 98 05 02 2 v 1 2 5 M ay 1 99 8 Infinite - Dimensional Linear Dynamical Systems with Chaoticity ∗
نویسندگان
چکیده
The authors present two results on infinite-dimensional linear dynamical systems with chaoticity. One is about the chaoticity of the backward shift map in the space of infinite sequences on a general Fréchet space. The other is about the chaoticity of a translation map in the space of real continuous functions. The chaos is shown in the senses of both Li-Yorke and Wiggins. Treating dimensions as freedoms, the two results imply that in the case of an infinite number of freedoms, a system may exhibit complexity even when the action is linear. Finally, the authors discuss physical applications of infinite-dimensional linear chaotic dynamical systems.
منابع مشابه
ar X iv : c ha o - dy n / 98 05 02 3 v 1 2 5 M ay 1 99 8 On a Linear Chaotic Quantum Harmonic Oscillator ∗ September 7 , 1997
Jinqiao Duan1 , Xin-Chu Fu2,3, Pei-De Liu4, and Anthony Manning2 1. Department of Mathematical Sciences, Clemson University, Clemson, South Carolina 29634, USA. 2. Mathematics Institute, University of Warwick, Coventry CV4 7AL, England, UK. 3. Wuhan Institute of Physics and Mathematics, The Chinese Academy of Sciences, P. O. Box 71010, Wuhan 430071, CHINA. 4. Department of Mathematics, Wuhan Un...
متن کاملar X iv : c ha o - dy n / 98 05 02 6 v 1 2 6 M ay 1 99 8 Chaotic Interaction of Langmuir Solitons and Long Wavelength Radiation
In this work we analyzed the interaction of isolated solitary structures and ion-acoustic radiation. If the radiation amplitude is small solitary structures persists, but when the amplitude grows energy transfer towards small spatial scales occurs. We show that transfer is particularly fast when a fixed point of a low dimensional model is destroyed.
متن کاملha o - dy n / 98 05 02 1 v 1 2 5 M ay 1 99 8 Passive Tracer Dispersion with Random or Periodic Source ∗
In this paper, the author investigates the impact of external sources on the pattern formation and long-time behavior of concentration profiles of passive tracers in a two-dimensional shear flow. It is shown that a time-periodic concentration profile exists for time-periodic external source, while for random source, the distribution functions of all concentration profiles weakly converge to a u...
متن کاملar X iv : c ha o - dy n / 99 11 02 5 v 1 1 8 N ov 1 99 9 General properties of propagation in chaotic systems
We conjecture that in one-dimensional spatially extended systems the propagation velocity of correlations coincides with a zero of the convective Lyapunov spectrum. This conjecture is successfully tested in three different contexts: (i) a Hamiltonian system (a Fermi-Pasta-Ulam chain of oscillators); (ii) a general model for spatio-temporal chaos (the complex Ginzburg-Landau equation); (iii) exp...
متن کامل