Intermittent two-point dynamics at the transition to chaos for random
 circle endomorphisms

Q: What type of study is this?

This is a Quantitative Study study.

Vincent P. H. Goverse; Ale Jan Homburg; Jeroen S. W. Lamb

doi:10.48550/arxiv.2503.08244

March 11, 2025Open Access

Intermittent two-point dynamics at the transition to chaos for random circle endomorphisms

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Key Points

Intermittent dynamics were observed at the transition to chaos, indicating a significant shift in behavior within the system.
The study found that the existence of infinite stationary measures corresponds to the transition from synchronisation to chaos.
Random circle endomorphisms with zero Lyapunov exponent were central to establishing the findings of this research.
The analysis provides deep insights into the dynamical characterization of systems nearing chaotic behavior.

Implication

Analysis reveals intermittent dynamics and infinite measures in circle endomorphisms, suggesting a link between synchronisation and chaos.

Abstract

We establish the existence of intermittent two-point dynamics and infinite stationary measures for a class of random circle endomorphisms with zero Lyapunov exponent, as a dynamical characterisation of the transition from synchronisation (negative Lyapunov exponent) to chaos (positive Lyapunov exponent).

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Cite This Study

Goverse et al. (2025) studied this question.

synapsesocial.com/papers/68da58c9c1728099cfd1096e https://doi.org/10.48550/arxiv.2503.08244

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Intermittent two-point dynamics at the transition to chaos for random circle endomorphisms

Key Points

Implication

Abstract

Discussion

Cite This Study

Intermittent two-point dynamics at the transition to chaos for random circle endomorphisms

Key Points

Implication

Abstract

Discussion

Cite This Study

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