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math.DS2025
Products of exact dynamical systems and Lorentzian continued fractions
Brandon G. Barreto-Rosa, Jean-Philippe Burelle, Anton Lukyanenko +1
We describe a new continued fraction system in Minkowski space , proving convergence, ergodicity with respect to an explicit invariant measure, and Lagrange's theo…
math.DS2023
Serendipitous decompositions of higher-dimensional continued fractions
Anton Lukyanenko, Joseph Vandehey
We prove a suite of dynamical results, including exactness of the transformation and piecewise-analyticity of the invariant measure, for a family of continued fraction systems, inc…
math.DS2018
Ergodicity of Iwasawa continued fractions via markable hyperbolic geodesics
Anton Lukyanenko, Joseph Vandehey
We prove the convergence and ergodicity of a wide class of real and higher-dimensional continued fraction algorithms, including folded and -type variants of complex, quaternioni…