Felipe Ramirez; Adam Fieldsteel; David Constantine
Diophantine approximation is a branch of number theory that concerns the metric relationship of the rationals and irrationals. Much of the present-day research in the subject approaches problems of approximation via dynamics. We introduce the Littlewood Conjecture, a longstanding problem that was almost completely proven in 2006 by a theorem of Einsiedler, Katok, and Lindenstrauss. After giving an exposition of classical Diophantine approxi- mation and fundamental ergodic theory, we set out a survey of the aforemen- tioned theorem's context, particularly the motivation of the authors' dynam- ical approach, rich connections to linear algebra and hyperbolic geometry, an exploration of measure rigidity, and an interpretation of the paper's main conclusions.
Chatha, Prayag George Singh, "Close Enough: a Dynamical Approach to the Littlewood Conjecture" (2017). Masters Theses. 149.
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