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Title: On exact statistics and classification of ergodic systems of integer dimension

We describe classes of ergodic dynamical systems for which some statistical properties are known exactly. These systems have integer dimension, are not globally dissipative, and are defined by a probability density and a two-form. This definition generalizes the construction of Hamiltonian systems by a Hamiltonian and a symplectic form. Some low dimensional examples are given, as well as a discretized field theory with a large number of degrees of freedom and a local nearest neighbor interaction. We also evaluate unequal-time correlations of these systems without direct numerical simulation, by Padé approximants of a short-time expansion. We briefly speculate on the possibility of constructing chaotic dynamical systems with non-integer dimension and exactly known statistics. In this case there is no probability density, suggesting an alternative construction in terms of a Hopf characteristic function and a two-form.
Authors:
;  [1] ;  [2] ;  [3]
  1. Department of Physics, Brown University, Providence, Rhode Island 02912 (United States)
  2. Harvard University, Center for Brain Science, Cambridge, Massachusetts 02138 (United States)
  3. (United States)
Publication Date:
OSTI Identifier:
22351117
Resource Type:
Journal Article
Resource Relation:
Journal Name: Chaos (Woodbury, N. Y.); Journal Volume: 24; Journal Issue: 2; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; CHAOS THEORY; CLASSIFICATION; COMPUTERIZED SIMULATION; CORRELATIONS; DEGREES OF FREEDOM; DENSITY; DYNAMICS; FIELD THEORIES; HAMILTONIANS; STATISTICS