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On the graph of the dimension function of the Lagrange and Markov spectra
Carlos Matheus, Carlos Gustavo Moreira, Polina Vytnova
We study the graph of the function encoding the Hausdorff dimensions of the classical Lagrange and Markov spectra with half-infinite lines of the form . For th…
New gaps on the Lagrange and Markov spectra
Luke Jeffreys, Carlos Matheus, Carlos Gustavo Moreira
Let and denote the Lagrange and Markov spectra, respectively. It is known that and that . In this work, we exhibit new gaps of …
Non-ergodicity on SU(2) and SU(3) character varieties of the once-punctured torus
Giovanni Forni, William Goldman, Sean Lawton +1
Utilizing KAM theory, we show that there are certain levels in relative SU(2) and SU(3) character varieties of the once-punctured torus where the action of a single hyperbolic elem…
Arithmeticity of the Kontsevich--Zorich monodromies of certain families of square-tiled surfaces
Etienne Bonnafoux, Manuel Kany, Pascal Kattler +5
The variations of Hodge structures of weight one associated to square-tiled surfaces naturally generate interesting subgroups of integral symplectic matrices called Kontsevich--Zor…