TY - JOUR
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
DO - 10.1016/0167-2789(83)90317-2
M3 - Article
AN - SCOPUS:0001375153
VL - 8
SP - 183
EP - 207
JO - Physica D: Nonlinear Phenomena
JF - Physica D: Nonlinear Phenomena
SN - 0167-2789
IS - 1-2
ER -