All but one expanding Lorenz maps with slope greater than or equal to are leo
Tom 176 / 2024
Colloquium Mathematicum 176 (2024), 193-206
MSC: Primary 37E05; Secondary 37B05
DOI: 10.4064/cm9382-10-2024
Opublikowany online: 25 November 2024
Streszczenie
We prove that with only one exception, all expanding Lorenz maps f:[0,1]\to [0,1] with f’(x)\ge \sqrt 2 (apart from a finite set of points) are locally eventually onto. Namely, for each such f and each nonempty open interval J\subset (0,1) there is n\in \mathbb N such that [0,1)\subset f^n(J). The exception is the map f_0(x)=\sqrt 2x+(2-\sqrt 2)/2 (mod 1). Recall that f is an expanding Lorenz map if it is strictly increasing on [0,c) and [c,1] for some c and satisfies inf f’ \gt 1.
