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ZENODO
Preprint . 2026
License: CC BY
Data sources: ZENODO
ZENODO
Preprint . 2026
License: CC BY
Data sources: Datacite
ZENODO
Preprint . 2026
License: CC BY
Data sources: Datacite
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Cierre modular y estructura 2-ádica interna en la dinámica de Collatz

Authors: Miguel Cerdá Bennassar;

Cierre modular y estructura 2-ádica interna en la dinámica de Collatz

Abstract

Se presenta un análisis estructural de la dinámica de Collatz basado en un cierre modular temprano y en el estudio de la valuación 2-ádica de los términos impares. Se demuestra que, tras el primer impar, las trayectorias quedan permanentemente excluidas de los múltiplos de 3 y confinadas a un ciclo modular rígido módulo 9. Dentro de este marco, la dinámica se reduce al análisis de los factores 3n+1 y de su valuación 2-ádica. Se introduce una descomposición sistemática de las trayectorias en tramos impares y colas pares, mostrando que la estructura global de la órbita —aunque no su duración exacta— queda determinada desde el valor inicial. El equilibrio entre episodios de crecimiento impar y divisiones por 2 se interpreta como una restricción estructural de la dinámica, sin recurrir a hipótesis probabilísticas ni argumentos heurísticos

Keywords

Dinámica discreta, Valuación 2-ádica, Tramos impares, Colas pares, Cierre modular, Dinámicas iterativas, Aritmética modular, Conjetura de Collatz

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
Average
Average
Average