Diophantine approximation for algebraic numbers
Advances in Homogeneous Dynamics May 11, 2015 - May 15, 2015
Location: MSRI: Simons Auditorium
transcendental number theory
homogeneous dynamics orbit
11Jxx - Diophantine approximation, transcendental number theory [See also 11K60]
11Kxx - Probabilistic theory: distribution modulo $1$; metric theory of algorithms
11K16 - Normal numbers, radix expansions, Pisot numbers, Salem numbers, good lattice points, etc. [See also 11A63]
37-XX - Dynamical systems and ergodic theory [See also 26A18, 28Dxx, 34Cxx, 34Dxx, 35Bxx, 46Lxx, 58Jxx, 70-XX]
37A20 - Orbit equivalence, cocycles, ergodic equivalence relations
A number is well approximable (WA) if the error when approximatin by p/q can be made small compared to the sqare of 1/q. Almost all reals are WA. For good reasons quadratic irrationals are not. Nothing is known for cubic irrationals. We show how this relates to special orbits in homogeneous dynamics.
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