Invariant Manifolds in the Measure-Preserving Mappings with Three-Dimensions

Details Invariant Manifolds in the Measure-Preserving Mappings with Three-Dimensions Invariant Manifolds in the Measure-Preserving Mappings with Three-Dimensions

Jun 1984

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1984cemec..33..111s&link_type=abstract

Celestial Mechanics, Volume 33, Issue 2, pp.111-125

Physics

13

Scientific paper

In this paper, we study the following three-dimensional mappings T:left\{ begin{gathered} x_{n + 1} = x_n + y_n + B sin z_n , \ y_{n + 1} = y_n + A sin x_{n + 1} , \ z_{n + 1} = z_n + C sin y_{n + 1} + D, \ right.left( {bmod 2Pi } right) where A, B, C, D are parameters. When D>BC and 2π/D is an irrational number, we find numerically-two-dimensional and one-dimensional invariant manifolds, but when DBC and 2π/D is a rational number we find numerically one-dimensional manifolds and the fixed points for some cycles.

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