Wildness of iteration of certain residue-class-wise affine mappings

DOI10.1016/j.aam.2006.08.003zbMath1146.11015OpenAlexW2020900260MaRDI QIDQ2465832

Stefan Kohl

Publication date: 9 January 2008

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

Full work available at URL: https://doi.org/10.1016/j.aam.2006.08.003

zbMATH Keywords

Collatz problem\(3n+1\) conjectureFurstenberg topologyresidue-class-wide affine mappingwildness criterion

Mathematics Subject Classification ID

Special sequences and polynomials (11B83) Continua theory in dynamics (37B45) Iteration of real functions in one variable (26A18) Arithmetic progressions (11B25) Sequences (mod (m)) (11B50) Connections of general topology with other structures, applications (54H99) Real rational functions (26C15)

Related Items

Algorithms for a class of infinite permutation groups. ⋮ ON CONJUGATES OF COLLATZ-TYPE MAPPINGS ⋮ An automated approach to the Collatz conjecture ⋮ A simple group generated by involutions interchanging residue classes of the integers. ⋮ An automated approach to the Collatz conjecture

Uses Software

• GAP
• RCWA

Cites Work

• Topologies related to arithmetical properties of integral domains
• Injectivity and surjectivity of Collatz functions
• Finite cycles of certain periodically linear permutations
• On the Infinitude of Primes
• The 3x + 1 Problem and Its Generalizations
• Iterates of Number Theoretic Functions with Periodic Rational Coefficients (Generalization of the 3x+ 1 Problem)
• ARITHMETICALLY RELATED IDEAL TOPOLOGIES AND THE INFINITUDE OF PRIMES

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