The analytic structure of dynamical systems and self-similar natural boundaries

Y. F. Chang; J. M. Greene; M. Tabor; J. Weiss

doi:10.1016/0167-2789(83)90317-2

The analytic structure of dynamical systems and self-similar natural boundaries

Y. F. Chang, J. M. Greene, M. Tabor, J. Weiss

Research output: Contribution to journal › Article › peer-review

53 Scopus citations

Abstract

In this paper we investigate the analytic, complex-time structure of the movable singularities for several dynamical systems. In general, it is found that there exists a direct connection between the occurencce of a certain type of multiple-valuedness of the singularities and the existence of a class of remarkable, "self-similar" natural boundaries for these systems. An asymptotic description of the distribution of singularities in the natural boundary is developed. This provides a description of the fine-scale structure of these natural boundaries that agrees closely with the numerical calculations.

Original language	English (US)
Pages (from-to)	183-207
Number of pages	25
Journal	Physica D: Nonlinear Phenomena
Volume	8
Issue number	1-2
DOIs	https://doi.org/10.1016/0167-2789(83)90317-2
State	Published - Jul 1983
Externally published	Yes

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics
Condensed Matter Physics
Applied Mathematics

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10.1016/0167-2789(83)90317-2

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@article{4a35786482a04b07bd610ebf21d7851a,

title = "The analytic structure of dynamical systems and self-similar natural boundaries",

abstract = "In this paper we investigate the analytic, complex-time structure of the movable singularities for several dynamical systems. In general, it is found that there exists a direct connection between the occurencce of a certain type of multiple-valuedness of the singularities and the existence of a class of remarkable, {"}self-similar{"} natural boundaries for these systems. An asymptotic description of the distribution of singularities in the natural boundary is developed. This provides a description of the fine-scale structure of these natural boundaries that agrees closely with the numerical calculations.",

author = "Chang, {Y. F.} and Greene, {J. M.} and M. Tabor and J. Weiss",

note = "Funding Information: In this paper we study the movable singularities of several dynamical systems and find, in general, that these singularities are multiple valued. The formal expansion of the solution about a singularity is developed, in detail, for the Hrnon-Heiles system. It is shown that a closed subset of the recursion relations defined by this expansion is associated * On leave from Dept. of Computer Science, University of Nebraska, Lincoln, Nebraska 68588. Present address: Dept. of Mathematics, San Diego State University, San Deigo, California, USA. ** Permanent address: Plasma Physics Laboratory, Princeton, New Jersey 08544, USA. t This work supported by Officeo f Naval Research, Contract No. N-00014-79-C-0537 and Department of Energy, Contract No. DOE-10923.",

year = "1983",

month = jul,

doi = "10.1016/0167-2789(83)90317-2",

language = "English (US)",

volume = "8",

pages = "183--207",

journal = "Physica D: Nonlinear Phenomena",

issn = "0167-2789",

publisher = "Elsevier B.V.",

number = "1-2",

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T1 - The analytic structure of dynamical systems and self-similar natural boundaries

AU - Chang, Y. F.

AU - Greene, J. M.

AU - Tabor, M.

AU - Weiss, J.

N1 - Funding Information: In this paper we study the movable singularities of several dynamical systems and find, in general, that these singularities are multiple valued. The formal expansion of the solution about a singularity is developed, in detail, for the Hrnon-Heiles system. It is shown that a closed subset of the recursion relations defined by this expansion is associated * On leave from Dept. of Computer Science, University of Nebraska, Lincoln, Nebraska 68588. Present address: Dept. of Mathematics, San Diego State University, San Deigo, California, USA. ** Permanent address: Plasma Physics Laboratory, Princeton, New Jersey 08544, USA. t This work supported by Officeo f Naval Research, Contract No. N-00014-79-C-0537 and Department of Energy, Contract No. DOE-10923.

PY - 1983/7

Y1 - 1983/7

N2 - In this paper we investigate the analytic, complex-time structure of the movable singularities for several dynamical systems. In general, it is found that there exists a direct connection between the occurencce of a certain type of multiple-valuedness of the singularities and the existence of a class of remarkable, "self-similar" natural boundaries for these systems. An asymptotic description of the distribution of singularities in the natural boundary is developed. This provides a description of the fine-scale structure of these natural boundaries that agrees closely with the numerical calculations.

AB - In this paper we investigate the analytic, complex-time structure of the movable singularities for several dynamical systems. In general, it is found that there exists a direct connection between the occurencce of a certain type of multiple-valuedness of the singularities and the existence of a class of remarkable, "self-similar" natural boundaries for these systems. An asymptotic description of the distribution of singularities in the natural boundary is developed. This provides a description of the fine-scale structure of these natural boundaries that agrees closely with the numerical calculations.

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U2 - 10.1016/0167-2789(83)90317-2

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JO - Physica D: Nonlinear Phenomena

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IS - 1-2

ER -

The analytic structure of dynamical systems and self-similar natural boundaries

Abstract

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