Badly approximable systems of affine forms, fractals, and Schmidt games

By Manfred Einsiedler, Jimmy Tseng. 2009

58 citations recorded by the source corpus.

Abstract A badly approximable system of affine forms is determined by a matrix and a vector. We show Kleinbock's conjecture for badly approximable systems of affine forms: for any fixed vector, the set of badly approximable systems of affine forms is winning (in the sense of Schmidt games) even when restricted to a fractal (from a certain large class of fractals). In addition, we consider fixing the matrix instead of the vector where an analog statement holds.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/bd9ce5e0250bccbfe8242ee8533e76aa8c9111a2

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Geometry and Topology

1. Mariusz Urba'nski
2. David Simmons
3. Lior Fishman

In Mathematical Physics

1. Mariusz Urba'nski
2. David Simmons
3. Lior Fishman
4. O. Sarig
5. V. Mayer

Citations in the corpus

• Diophantine approximation and the geometry of limit sets in Gromov hyperbolic metric spaces (2013, background): “Note that winning sets arise naturally in many settings in dynamics and Diophantine approximation [21, 22, 23, 27, 30, 31, 47, 49, 58, 70, 71, 80, 81].”
• The set of badly approximable vectors is strongly C1 incompressible (2011, unknown): “1”