On the Measure-Preserving Mappings with Odd Dimension

Details On the Measure-Preserving Mappings with Odd Dimension On the Measure-Preserving Mappings with Odd Dimension

May 1983

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1983cemec..30....7s&link_type=abstract

Celestial Mechanics, Volume 30, Issue 1, pp.7-19

Physics

15

Scientific paper

In this paper, using two methods: LCN'S (Lyapunov characteristic numbers) method and slice cutting method, we study numerically two mappings with odd dimension: T_1 :left\{ {begin{array}{*{20}c} {x_{n + 1} = x_n + z_n ,} \ {y_{n + 1} = y_n + x_{n + 1} , (bmod 2π )} \ {z_{n + 1} = z_n + Asin y_{n + 1} ,} \ } right. T_2 :left\{ {begin{array}{*{20}c} {x_{n + 1} = x_n + y_n + B sin z_n ,} \ {y_{n + 1} = y_n + A sin x_{n + 1} , (bmod 2π ),} \ {z_{n + 1} = z_n + B sin y_{n + 1} ,} \ } right. whereA, B are parameters. For the mappingT 1 the whole region is stochastic; however, we find two-dimensional invariant manifolds for the mappingT 2.

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