m-transitivity and Li–Yorke n-chaos

Jingmin Pi and Qigui Yang

Chaos, Solitons & Fractals, 2026, vol. 210, issue P2

Abstract: Chaotic dynamics plays a fundamental role both in addressing Smale’s fourteenth problem for the twenty-first century and in the design of complex engineering cybernetic systems. To enable a deeper exploration of high-dimensional chaos, this paper introduces the concept of transitivity with respect to order in non-autonomous discrete systems (NADSs), referred to as m-transitivity for m≥1. The invariance of m-transitivity is first investigated, leading to the following conclusions: (1) In finitely generated and surjective NADSs, transitivity of all orders is preserved under iteration; (2) In a special class of NADSs with collective convergence, m-transitivity of the original system is inherited by its limit system; (3) In feebly open and surjective NADSs, m-transitivity is invariant under time-shifts. Finally, it is demonstrated that m-transitive NADSs can exhibit complex dynamical behavior. Specifically, n-transitivity implies Li–Yorke n-chaos for n≥2.

Keywords: High-dimensional chaos; m-transitivity; Li–Yorke n-chaos; Non-autonomous discrete systems; Invariance (search for similar items in EconPapers)
Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:210:y:2026:i:p2:s0960077926008398

DOI: 10.1016/j.chaos.2026.118698

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