Semi-Poisson nearest-neighbor distance statistics for a 2D dissipative map

Abstract

Typical pseudotrajectories of 2D ergodic maps are known to possess Wignerian nearest-neighbor distance distributions (NNDDs). In the case of 2D chaotic dissipative maps, bounded aperiodic pseudotrajectories typically evolve on planar strange attractors. In this microarticle, the hypothesis that such pseudotrajectories should possess NNDDs that are intermediate between the Poisson and Wigner distributions is put forward and a rare example for which the intermediate distribution can be clearly identified is presented. In particular, it is demonstrated numerically that typical pseudotrajectories evolving in the strange attractor of the standard 2D Ikeda map possess semi-Poissionian NNDDs.

Keywords

• 2D chaotic maps
• 2D dissipative maps
• Chaotic trajectories
• Geometrical statistics
• Nearest-neighbor distances
• Semi-Poisson distribution