Franck Coppi

Rigidity, Extremal Words, and Diophantine Obstructions for the Accelerated Collatz Map

Rigidity, Extremal Words, and Diophantine Obstructions for the Accelerated Collatz Map (v12) We study the accelerated Collatz (Syracuse) map through its symbolic coding by words of 2-adic valuations. We prove that the natural invariant measure is ergodic and is the unique invaria...

Rigidity, Extremal Words, and Diophantine Obstructions for the Accelerated Collatz Map

Rigidity, Extremal Words, and Diophantine Obstructions for the Accelerated Collatz Map (v12) We study the accelerated Collatz (Syracuse) map through its symbolic coding by words of 2-adic valuations. We prove that the natural invariant measure is ergodic and is the unique invaria...

Rigidity, Extremal Words, and Diophantine Obstructions for the Accelerated Collatz Map

We study the accelerated Collatz (Syracuse) map T on the odd positive integers, T(n) = (3n+1)/2^v2(3n+1), through its symbolic coding by finite words of 2-adic valuations. First, using the classical conjugacy between the 2-adic extension of the (non-accelerated) Collatz map and t...