Low emergence in one-dimensional dynamics
We show that every $C^2$ immersion of the circle $\mathbb{S}^1$ into itself has low emergence.
math.DS↗
arXiv subjects
Odylo Costa
Publications and source records attributed to Odylo Costa.
A periodic flow with high emergence
We construct a smooth nonsingular periodic flow on a compact manifold with high emergence, in sharp contrast with the low statistical complexity of periodic self-maps. The construction is based on a modification of the Epstein--Vogt counterexample to the Periodic Orbit Conjecture and on the high-emergence mechanism of Berger--Bochi.
math.DS↗