Optimal Rational Approximation Number Sets: Application to Nonlinear Dynamics in Particle Accelerators

Nicholas J. Daras () and Michael N. Vrahatis ()
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Nicholas J. Daras: Hellenic Army Academy, Department of Mathematics
Michael N. Vrahatis: University of Patras, Department of Mathematics

A chapter in Contributions in Mathematics and Engineering, 2016, pp 95-115 from Springer

Abstract: Abstract We construct optimal multivariate vectors of rational approximation numbers with common denominator and whose coordinate decimal expansion string of digits coincides with the decimal expansion digital string of a given sequence of mutually irrational numbers as far as possible. We investigate several numerical examples and we present an application in Nuclear Physics related to the beam stability problem of particle beams in high-energy hadron colliders.

Keywords: Simultaneous Rational Approximations; Beam Stability Problems; Decimal Expansion; Irrational Number; Jacobi-Perron Algorithm (search for similar items in EconPapers)
Date: 2016
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-31317-7_6

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DOI: 10.1007/978-3-319-31317-7_6

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