Switched Server Systems Whose Parameters are Normal Numbers in Base 4

Amaral, Antunes, Andre do; Bugeaud, Yann; Pires, Benito

doi:10.1007/s12346-022-00679-7

Qual. Theory Dyn. Syst.

2022

DOI: 10.1007/s12346-022-00679-7

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Switched Server Systems Whose Parameters are Normal Numbers in Base 4

Antunes, Andre do Amaral

Yann Bugeaud

Benito Pires

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2024

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Rotation number of 2-interval piecewise affine maps

Gaivão,

Laurent,

Nogueira

2024

Aequat. Math.

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We study maps of the unit interval whose graph is made up of two increasing segments and which are injective in an extended sense. Such maps $$f_{\varvec{p}}$$ f p are parametrized by a quintuple $$\varvec{p}$$ p of real numbers satisfying inequations. Viewing $$f_{\varvec{p}}$$ f p as a circle map, we show that it has a rotation number $$\rho (f_{\varvec{p}})$$ ρ ( f p ) and we compute $$\rho (f_{\varvec{p}})$$ ρ ( f p ) as a function of $$\varvec{p}$$ p in terms of Hecke–Mahler series. As a corollary, we prove that $$\rho (f_{\varvec{p}})$$ ρ ( f p ) is a rational number when the components of $$\varvec{p}$$ p are algebraic numbers.

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Rotation number of 2-interval piecewise affine maps

Gaivão,

Laurent,

Nogueira

2024

Aequat. Math.

View full text Add to dashboard Cite

show abstract

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Switched Server Systems Whose Parameters are Normal Numbers in Base 4

Cited by 1 publication

References 22 publications

Rotation number of 2-interval piecewise affine maps

Rotation number of 2-interval piecewise affine maps

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