Lagrange and Markov spectra for typical smooth systems
arXiv:2311.05763
Abstract
We prove that among the set of smooth diffeomorphisms there exists a -open and dense subset of data such that either the Lagrange spectrum is finite and the dynamics is a Morse-Smale diffeomorphism or the Lagrange spectrum has positive Hausdorff dimension and the system has positive topological entropy.
31 pages