|Nov 08, 2018
The Lagrange spectrum is the set of approximation constants in the Diophantine approximation for badly approximated numbers. It is closely related with the Markov spectrum which corresponds the minimum values of indefinite quadratic forms over integral vectors. We discuss the Diophantine approximation for the rational points in the unit circle. We will introduce a dynamical system originally defined by Romik in 2008, study its Lagrange and Markov spectra.