The Ergodicity of the Collatz Process in Positive Integer Field
The $3 x+ 1$ problem, also called the Collatz conjecture, is a very interesting unsolved
mathematical problem related to computer science. This paper generalized this problem by
relaxing the constraints, ie, generalizing this deterministic process to non-deterministic
process, and set up three models. This paper analyzed the ergodicity of these models and
proved that the ergodicity of the Collatz process in positive integer field holds, ie, all the
positive integers can be transformed to 1 by the iterations of the Collatz function.
mathematical problem related to computer science. This paper generalized this problem by
relaxing the constraints, ie, generalizing this deterministic process to non-deterministic
process, and set up three models. This paper analyzed the ergodicity of these models and
proved that the ergodicity of the Collatz process in positive integer field holds, ie, all the
positive integers can be transformed to 1 by the iterations of the Collatz function.
The problem, also called the Collatz conjecture, is a very interesting unsolved mathematical problem related to computer science. This paper generalized this problem by relaxing the constraints, i.e., generalizing this deterministic process to non-deterministic process, and set up three models. This paper analyzed the ergodicity of these models and proved that the ergodicity of the Collatz process in positive integer field holds, i.e., all the positive integers can be transformed to 1 by the iterations of the Collatz function.
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