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March 7, 2026Open Access

VIII. Return map, rigid regime, and invariance gap in the 2-adic Collatz dynamics

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Authors

MBMiguel Cerdá Bennassar

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Overview

This work analyzes the return map and invariant gaps in 2-adic Collatz dynamics, suggesting implications for orbit survival.

Key Points

  • This work aims to understand how the structural properties of 2-adic Collatz dynamics affect orbit persistence.
  • Proposed a structural reduction of Collatz dynamics to an autonomous system in 2-adic integers.
  • Formalized the concept of rigid regime and analyzed the circumstances under which orbits persist.
  • Established a dichotomy based on escape and stationary regimes, focusing on convergence behaviors.
  • The persistence of infinite orbits depends on the return map structure.
  • Two key regimes (escape and stationary) lead to specific convergence behaviors towards -1.
  • Identified a significant gap in non-invariance related to resonant cylinders and its impact on ergodic components.

Cite This Study

Miguel Cerdá Bennassar (2026) studied this question.

synapsesocial.com/papers/69abc2725af8044f7a4ec221https://doi.org/10.5281/zenodo.18879361
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