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Iterates of Number Theoretic Functions with Periodic Rational Coefficients (Generalization of the 3x+ 1 Problem)

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Publication:3993680
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DOI10.1002/sapm1992863185zbMath0773.11019OpenAlexW2282992823MaRDI QIDQ3993680

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Publication date: 3 August 1992

Published in: Studies in Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/sapm1992863185


zbMATH Keywords

cyclesergodic propertiesCollatz functiongeneralization of the \(3x+1\) problem


Mathematics Subject Classification ID

Special sequences and polynomials (11B83)


Related Items (3)

Injectivity and surjectivity of Collatz functions ⋮ A remark about the density of the orbits of the Collatz permutation ⋮ Wildness of iteration of certain residue-class-wise affine mappings



Cites Work

  • Unnamed Item
  • Iteration of the number-theoretic function \(f(2n)=n\), \(f(2n+1)=3n+2\)
  • A Markov process underlying the generalized Syracuse algorithm
  • A Markov approach to the generalized Syracuse algorithm
  • The 3x + 1 Problem and Its Generalizations
  • On some Markov matrices arising from the generalized Collatz mapping
  • A generalization of Hasse's generalization of the Syracuse algorithm


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