Dynamical Systems, Fractal Geometry and Diophantine Approximations
Carlos Gustavo Tamm de Araujo Moreira
TL;DR
This survey explores the interconnections between fractal geometry, dynamical systems, and Diophantine approximations, highlighting recent advances in understanding the geometric properties of classical spectra and their generalizations.
Contribution
It provides a comprehensive overview of recent results linking fractal geometry, dynamical systems, and Diophantine approximations, including new insights into spectra and geometric properties.
Findings
Recent results on Markov and Lagrange spectra
Generalizations in dynamical systems and differential geometry
Descriptions of geometric properties of spectra
Abstract
We describe in this survey several results relating Fractal Geometry, Dynamical Systems and Diophantine Approximations, including a description of recent results related to geometrical properties of the classical Markov and Lagrange spectra and generalizations in Dynamical Systems and Differential Geometry.
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Taxonomy
TopicsMathematical Dynamics and Fractals · Advanced Mathematical Theories and Applications · Quantum chaos and dynamical systems