Work

Simultaneous dense and nondense orbits for commuting maps

Year: 2013

Type: preprint

Abstract: We show that, for two commuting automorphisms of the torus and for two elements of the Cartan action on compact higher rank homogeneous spaces, many points have drastically different orbit structures for the two maps. Specifically, using measure rigidity, we show that the set of points that have dense orbit under one map and nondense orbit under the second has full Hausdorff dimension.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.1309.4823

Authors: Bergelson, Vitaly, Einsiedler, Manfred, Tseng, Jimmy

Institutions: The Ohio State University, ETH Zurich, University of Bristol

Language: English

Topic: Mathematical Dynamics and Fractals

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, European Commission, Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung

Awards: Applications of Ergodic Theory to Combinatorics and Number Theory, G3207356259, Equidistribution and dynamics on homogeneous spaces, G7553243680, G878044590, G896728979, G993971353

OpenAlex ID: W2951175366

Cites: 28

Cited by: 2

Related to: 20