PreprintarXiv licencearXiv
Ergodicity of dynamical systems without uniqueness of orbits
Abstract
Recently, there has been considerable interest in the study of non-deterministic dynamical systems. To analyze the chaotic behavior of such systems from a measure-theoretic viewpoint, it is desirable to consider ergodicity. However, the classical definition of ergodicity involves invariant sets, whose definition is not unique for non-deterministic dynamical systems. Thus, we are led to the question of which invariance yields an interesting definition of ergodicity. Here, we propose a definition based on the strong backward invariance and show that analogs of classical results hold. We also consider implications of the Birkhoff ergodic theorem for systems without uniqueness of orbits.
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BibTeX
@misc{suda2026ergodicity,
title = {{Ergodicity of dynamical systems without uniqueness of orbits}},
author = {Tomoharu Suda},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.11087},
eprint = {2609.11087},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.11087},
}
RIS
TY - UNPB
TI - Ergodicity of dynamical systems without uniqueness of orbits
AU - Tomoharu Suda
PY - 2026
DA - 2026/09/10
PB - arXiv
DO - 10.48550/arxiv.2609.11087
UR - https://arxiv.org/abs/2609.11087
AB - Recently, there has been considerable interest in the study of non-deterministic dynamical systems. To analyze the chaotic behavior of such systems from a measure-theoretic viewpoint, it is desirable to consider ergodicity. However, the classical definition of ergodicity involves invariant sets, whose definition is not unique for non-deterministic dynamical systems. Thus, we are led to the question of which invariance yields an interesting definition of ergodicity. Here, we propose a definition based on the strong backward invariance and show that analogs of classical results hold. We also consider implications of the Birkhoff ergodic theorem for systems without uniqueness of orbits.
ER -