Simultaneous Diophantine approximation of the dynamical systems x2 and x3
报告题目：Simultaneous Diophantine approximation of the dynamical systems x2 and x3
摘要：We are interested in the simultaneous Diophantine approximation problem of the dynamical systems x2 module one and x3 modulo one on the unit interval. Precisely, we study the size of the sets of points whose orbits under the dynamical systems x2 and x3 simultaneously approach to a given point with a given speed. A zero-one law for the Lebesgue measure of such sets is proved. The Hausdorff dimension formula is also obtained for the approximation of exponential speed. We underline that one part of the dimensional formula is established under the famous abc conjecture. This is a joint work with Bing Li, Sanju Velani and Evgeniy Zorin.