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

TL;DR

This paper investigates the nearest-neighbor distance distributions of pseudotrajectories in 2D dissipative maps, revealing that they follow semi-Poissonian distributions, which are intermediate between Poisson and Wigner distributions.

Contribution

It introduces the hypothesis that dissipative 2D map pseudotrajectories have intermediate NNDDs and provides numerical evidence using the Ikeda map as a clear example.

Findings

Pseudotrajectories on strange attractors exhibit semi-Poissonian NNDDs.

Numerical analysis confirms the intermediate distribution in the Ikeda map.

The results suggest a new statistical characterization of dissipative chaotic systems.

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.