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- Title
Persistent Non-statistical Dynamics in One-Dimensional Maps.
- Authors
Coates, Douglas; Luzzatto, Stefano
- Abstract
We study a class F ^ of one-dimensional full branch maps introduced in Coates et al. (Commun Math Phys 402(2):1845–1878, 2023), admitting two indifferent fixed points as well as critical points and/or singularities with unbounded derivative. We show that F ^ can be partitioned into 3 pairwise disjoint subfamilies F ^ = F ∪ F ± ∪ F ∗ such that all g ∈ F have a unique physical measure equivalent to Lebesgue, all g ∈ F ± have a physical measure which is a Dirac- δ measure on one of the (repelling) fixed points, and all g ∈ F ∗ are non-statistical and in particular have no physical measure. Moreover we show that these subfamilies are intermingled: they can all be approximated by maps in the other subfamilies in natural topologies.
- Publication
Communications in Mathematical Physics, 2024, Vol 405, Issue 4, p1
- ISSN
0010-3616
- Publication type
Article
- DOI
10.1007/s00220-024-04957-0