Simultaneously bounded and dense orbits for commuting Cartan actions

Abstract: With the goal to attack Uniform Littlewood’s Conjecture proposed in [BFK25], we introduced the concept of “fiberwise nondivergence” for the action of a cone inside the full diagonal subgroup of SL_3(R). Then it is proved in our paper that there exists a dense subset of SL_3(R)/SL_3(Z) in which each point has a fiberwise non-divergent orbit under a cone inside the full diagonal subgroup and an unbounded orbit under every diagonal flow. Our proof also presented the first instance of results concerning simultaneously bounded and dense orbits for commuting actions on noncompact spaces. This is a joint work with Dmitry Kleinbock.

dynamical systemsnumber theory

Audience: general audience

New England Dynamics and Number Theory Seminar