Analogues of the 3 x + Problem in Polynomial Rings of Characteristic 2

作者：Nichols Daniel^*

来源：Experimental Mathematics, 2018, 27(1): 100-110.

DOI：10.1080/10586458.2016.1227734

• Collatz conjecture
• discrete dynamical system
• random walk
• 3 x+1

The Collatz conjecture (also known as the 3x + 1 problem) concerns the behavior of the discrete dynamical system on the positive integers defined by iteration of the so-called 3x + 1 function. We investigate analogous dynamical systems in rings of functions of algebraic curves over F-2. We prove in this setting a generalized analogue of a theorem of Terras concerning the asymptotic distribution of stopping times. We also present experimental data on the behavior of these dynamical systems.

• 出版日期2018