English

Lagrange and Markov spectra for typical smooth systems

Dynamical Systems 2023-11-13 v1

Abstract

We prove that among the set of smooth diffeomorphisms there exists a C1C^1-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.

Keywords

Cite

@article{arxiv.2311.05763,
  title  = {Lagrange and Markov spectra for typical smooth systems},
  author = {Jamerson Bezerra and Carlos Gustavo Moreira and Sandoel Vieira},
  journal= {arXiv preprint arXiv:2311.05763},
  year   = {2023}
}

Comments

31 pages

R2 v1 2026-06-28T13:16:53.474Z