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Abstract
A symmetric Lorenz map is obtained by ‘flipping’ one of the two branches of a symmetric unimodal map. We use this to derive a Sharkovsky-like theorem for symmetric Lorenz maps, and also to find cases where the unimodal map restricted to the critical omega-limit set is conjugate to a Sturmian shift. This has connections with properties of unimodal inverse limit spaces embedded as attractors of some planar homeomorphisms.
MATHEMATICS SUBJECT CLASSIFICATIONS 2010:
Disclosure statement
No potential conflict of interest was reported by the author(s).
Notes
1 Its statement was suggested to us by Boyland, de Carvalho, Hall through personal communication.
Additional information
Funding
AA was supported by grant 2018/17585-5, São Paulo Research Foundation (FAPESP). HB gratefully acknowledges the support of the FWF stand-alone grant number P31950-N45. JČ was supported by the FWF Schrödinger Fellowship stand-alone project J 4276-N35 and University of Ostrava grant IRP201824 ‘Complex topological structures’; Austrian Science Fund (J-4276,P31950-N45).