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arXiv · 2311.05763

Lagrange and Markov spectra for typical smooth systems

Jamerson Bezerra·Carlos Gustavo Moreira·Sandoel Vieira
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Abstract

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

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Jamerson Bezerra, Carlos Gustavo Moreira, Sandoel Vieira. 2023-11-09. Lagrange and Markov spectra for typical smooth systems. https://arxiv.org/abs/2311.05763

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