PreprintCC BY-NC-ND 4.0arXiv
Weak mixing for dynamical systems with ℳα-shadowing
Abstract
This paper studies weak mixing for two classes of dynamical systems with the ℳα-shadowing property using the generic factor characterization of weak scattering. First, for every α∈[0,1), every M-system with the ℳα-shadowing property is weakly mixing, thereby answering [P. Oprocha et. al., On partial shadowing of complete pseudo-orbits, J. Math. Anal. Appl., Question~1] negatively. Second, for every α∈(0,1), the ℳα-shadowing property implies weak mixing for E-systems and, in particular, for dynamical systems whose measure center is the whole space.Finally, an E-system with the ℳ0-shadowing property which is not weakly mixing is constructed, showing that the parameter range α∈(0,1) in the E-system result is optimal.
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BibTeX
@misc{wu2026weak,
title = {{Weak mixing for dynamical systems with $\bm\mathscr M_\bmα$-shadowing}},
author = {Xinxing Wu and Jidan Wei and Xu Zhang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.31724},
eprint = {2609.31724},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.31724},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Weak mixing for dynamical systems with ℳ_α-shadowing
AU - Xinxing Wu
AU - Jidan Wei
AU - Xu Zhang
PY - 2026
DA - 2026/09/22
PB - arXiv
DO - 10.48550/arxiv.2609.31724
UR - https://arxiv.org/abs/2609.31724
AB - This paper studies weak mixing for two classes of dynamical systems with the ℳ_α-shadowing property using the generic factor characterization of weak scattering. First, for every α∈[0,1), every M-system with the ℳ_α-shadowing property is weakly mixing, thereby answering [P. Oprocha et. al., On partial shadowing of complete pseudo-orbits, J. Math. Anal. Appl., Question~1] negatively. Second, for every α∈(0,1), the ℳ_α-shadowing property implies weak mixing for E-systems and, in particular, for dynamical systems whose measure center is the whole space.Finally, an E-system with the ℳ_0-shadowing property which is not weakly mixing is constructed, showing that the parameter range α∈(0,1) in the E-system result is optimal.
ER -