Dyadic Diophantine approximation and Katok's horseshoe approximation
نویسندگان
چکیده
منابع مشابه
Diophantine approximation and Diophantine equations
The first course is devoted to the basic setup of Diophantine approximation: we start with rational approximation to a single real number. Firstly, positive results tell us that a real number x has “good” rational approximation p/q, where “good” is when one compares |x − p/q| and q. We discuss Dirichlet’s result in 1842 (see [6] Course N◦2 §2.1) and the Markoff–Lagrange spectrum ([6] Course N◦1...
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15 صفحه اولMultiplicative Diophantine approximation
In his paper, Dirichlet gives a complete proof for n = 1 and observes that this proof can be easily extended to arbitrary values of n. Good references on this topic are Chapter II of [52] and Cassels’ book [17]. There are in the literature many papers on various generalisations of the Dirichlet Theorem and on closely related problems. A typical question asks whether for a given set of mn real n...
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In this article we formalize some results of Diophantine approximation, i.e. the approximation of an irrational number by rationals. A typical example is finding an integer solution (x, y) of the inequality |xθ − y| ¬ 1/x, where θ is a real number. First, we formalize some lemmas about continued fractions. Then we prove that the inequality has infinitely many solutions by continued fractions. F...
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ژورنال
عنوان ژورنال: Acta Arithmetica
سال: 2008
ISSN: 0065-1036,1730-6264
DOI: 10.4064/aa132-3-2