English

Minimal Random Attractors

Dynamical Systems 2017-12-27 v1

Abstract

It is well-known that random attractors of a random dynamical system are generally not unique. We show that for general pullback attractors and weak attractors, there is always a minimal (in the sense of smallest) random attractor which attracts a given family of (possibly random) sets. We provide an example which shows that this property need not hold for forward attractors. We point out that our concept of a random attractor is very general: The family of sets which are attracted is allowed to be completely arbitrary.

Keywords

Cite

@article{arxiv.1712.08692,
  title  = {Minimal Random Attractors},
  author = {Hans Crauel and Michael Scheutzow},
  journal= {arXiv preprint arXiv:1712.08692},
  year   = {2017}
}

Comments

19 pages

R2 v1 2026-06-22T23:27:56.986Z