On the complexity of a putative counterexample to the -adic Littlewood conjecture

DOI10.1112/S0010437X15007393zbMath1331.11049arXiv1405.5545WikidataQ123020599 ScholiaQ123020599MaRDI QIDQ3447684

Dmitry Badziahin, Manfred Einsiedler, Yann Bugeaud, Dmitry Kleinbock

Publication date: 27 October 2015

Published in: Compositio Mathematica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1405.5545

zbMATH Keywords

complexityDiophantine approximationcontinued fractionsLittlewood conjecturemeasure rigidity

Mathematics Subject Classification ID

Entropy and other invariants, isomorphism, classification in ergodic theory (37A35) Metric theory (11J83) Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.) (37D40) Homogeneous approximation to one number (11J04) Approximation in non-Archimedean valuations (11J61)

Related Items (7)

On the \(t\)-adic Littlewood conjecture ⋮ Cantor-winning sets and their applications ⋮ On certain simultaneous rational approximations in \(\mathbb{R}^2\) and certain rational approximations in \(\mathbb{Q}_p\) ⋮ Reformulating the \(p\)-adic Littlewood conjecture in terms of infinite loops mod \(p^k\) ⋮ A note on the base-\(p\) expansions of putative counterexamples to the \(p\)-adic Littlewood conjecture ⋮ The Möbius transformation of continued fractions with bounded upper and lower partial quotients ⋮ On the multiples of a badly approximable vector

Cites Work

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• Automatic Sequences
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• On a mixed Littlewood conjecture in Diophantine approximation
• Symbolic Dynamics
• Symbolic Dynamics II. Sturmian Trajectories
• On the product of three homogeneous linear forms and indefinite ternary quadratic forms
• On a problem in simultaneous Diophantine approximation: Littlewood's conjecture

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