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Title: Linear vs nonlinear and infinite vs finite: An interpretation of chaos

Abstract

An example of a linear infinite-dimensional system is presented that exhibits deterministic chaos and thus challenges the presumably unquestionable connection between chaos and nonlinearity. Via this example, the roles of, and relationships between, linearity, nonlinearity, infinity and finiteness in the occurrence of chaos are investigated. The analysis of these complementary but related aspects leads to: a new interpretation of chaos as the manifestation of incompressible and thus incompressible information and a conjecture about the nonexistence of operationally accessible linear systems.

Authors:
Publication Date:
Research Org.:
Oak Ridge National Lab., TN (USA)
Sponsoring Org.:
DOE/ER
OSTI Identifier:
6502672
Report Number(s):
ORNL/TM-11667
ON: DE91002522
DOE Contract Number:
AC05-84OR21400
Resource Type:
Technical Report
Country of Publication:
United States
Language:
English
Subject:
99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; RANDOMNESS; STATISTICAL MODELS; DYNAMICS; NONLINEAR PROBLEMS; MATHEMATICAL MODELS; MECHANICS; 990200* - Mathematics & Computers

Citation Formats

Protopopescu, V. Linear vs nonlinear and infinite vs finite: An interpretation of chaos. United States: N. p., 1990. Web. doi:10.2172/6502672.
Protopopescu, V. Linear vs nonlinear and infinite vs finite: An interpretation of chaos. United States. doi:10.2172/6502672.
Protopopescu, V. Mon . "Linear vs nonlinear and infinite vs finite: An interpretation of chaos". United States. doi:10.2172/6502672. https://www.osti.gov/servlets/purl/6502672.
@article{osti_6502672,
title = {Linear vs nonlinear and infinite vs finite: An interpretation of chaos},
author = {Protopopescu, V.},
abstractNote = {An example of a linear infinite-dimensional system is presented that exhibits deterministic chaos and thus challenges the presumably unquestionable connection between chaos and nonlinearity. Via this example, the roles of, and relationships between, linearity, nonlinearity, infinity and finiteness in the occurrence of chaos are investigated. The analysis of these complementary but related aspects leads to: a new interpretation of chaos as the manifestation of incompressible and thus incompressible information and a conjecture about the nonexistence of operationally accessible linear systems.},
doi = {10.2172/6502672},
journal = {},
number = ,
volume = ,
place = {United States},
year = {Mon Oct 01 00:00:00 EDT 1990},
month = {Mon Oct 01 00:00:00 EDT 1990}
}

Technical Report:

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  • The properties of charged-particle motion in Hamiltonian dynamics are studied in a magnetotail-like magnetic-field configuration. It is shown by numerical integration of the equation of motion that the system is generally nonintegrable and that the particle motion can be classified into three distinct types of orbits; the bounded integrable orbits, unbounded stochastic orbits and unbounded transient orbits. It is also shown that different regions of the phase space exhibit qualitatively different response to external influences. The concept of differential memory in single-particle distributions is proposed. Physical implications to the dynamical properties of the magnetotail plasmas, and the possible generation ofmore » non-Maxwellian features in the distribution function are discussed.« less
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