Work

Lagrange and Markov spectra for typical smooth systems

Year: 2025

Type: article

Abstract: We prove that among the set of pairs ( $C^2$ -diffeomorphism, $C^1$ -potential), there exists a $C^1$ -open and dense subset 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. We also prove that such dichotomy does not hold for typical systems when replacing the Lagrange by the Markov spectrum.

Source: Ergodic Theory and Dynamical Systems

DOI: 10.1017/etds.2025.10247

Authors: JAMERSON BEZERRA, CARLOS GUSTAVO MOREIRA, SANDOEL VIEIRA

Institutions: Nicolaus Copernicus University, Instituto Nacional de Matemática Pura e Aplicada, Universidade Federal do Piauí

Language: English

Topic: Mathematical Dynamics and Fractals

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Narodowe Centrum Nauki, Fundação para a Ciência e a Tecnologia

Awards: G2881537184, Novas Tendências em expoentes de Lyapunov