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Title: Logarithmic singularities and chaotic behavior in Hamiltonian systems

Abstract

Several connections have been recently discovered between the real time behavior of the solution of dynamical systems and their movable singularities in the complex time plane. One of them has led to a direct method for identifying integrable Hamiltonian and dissipative systems by requiring that they possess the Painleve property, i.e. that their general solutions have no movable singularities other than poles. In this paper we further explore these connections by partially lifting the Painleve property and admitting logarithmic singularities. We find in a number of interesting Hamiltonian examples, that admitting only ln(t-t/sub 0/) terms still implies globally ''regular'' motion and very little chaos, whereas more complicated singularities of the type lnln(t-t/sub 0/) are associated with the presence of large scale regions of chaotic behavior.

Authors:
;
Publication Date:
Research Org.:
Mathematics and Computer Science, Clarkson College of Technology, Potsdam, New York 13676
OSTI Identifier:
7038077
DOE Contract Number:  
AC03-77ER01538
Resource Type:
Journal Article
Journal Name:
AIP Conf. Proc.; (United States)
Additional Journal Information:
Journal Volume: 88:1
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; EQUATIONS OF MOTION; ANALYTICAL SOLUTION; HAMILTONIAN FUNCTION; INTEGRALS; SINGULARITY; DIFFERENTIAL EQUATIONS; EQUATIONS; FUNCTIONS; PARTIAL DIFFERENTIAL EQUATIONS; 657002* - Theoretical & Mathematical Physics- Classical & Quantum Mechanics; 658000 - Mathematical Physics- (-1987)

Citation Formats

Bountis, T, and Segur, H. Logarithmic singularities and chaotic behavior in Hamiltonian systems. United States: N. p., 1982. Web. doi:10.1063/1.33639.
Bountis, T, & Segur, H. Logarithmic singularities and chaotic behavior in Hamiltonian systems. United States. https://doi.org/10.1063/1.33639
Bountis, T, and Segur, H. 1982. "Logarithmic singularities and chaotic behavior in Hamiltonian systems". United States. https://doi.org/10.1063/1.33639.
@article{osti_7038077,
title = {Logarithmic singularities and chaotic behavior in Hamiltonian systems},
author = {Bountis, T and Segur, H},
abstractNote = {Several connections have been recently discovered between the real time behavior of the solution of dynamical systems and their movable singularities in the complex time plane. One of them has led to a direct method for identifying integrable Hamiltonian and dissipative systems by requiring that they possess the Painleve property, i.e. that their general solutions have no movable singularities other than poles. In this paper we further explore these connections by partially lifting the Painleve property and admitting logarithmic singularities. We find in a number of interesting Hamiltonian examples, that admitting only ln(t-t/sub 0/) terms still implies globally ''regular'' motion and very little chaos, whereas more complicated singularities of the type lnln(t-t/sub 0/) are associated with the presence of large scale regions of chaotic behavior.},
doi = {10.1063/1.33639},
url = {https://www.osti.gov/biblio/7038077}, journal = {AIP Conf. Proc.; (United States)},
number = ,
volume = 88:1,
place = {United States},
year = {1982},
month = {7}
}