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Full-Text Articles in Dynamical Systems
Disjointness Of Linear Fractional Actions On Serre Trees, Henry W. Talbott
Disjointness Of Linear Fractional Actions On Serre Trees, Henry W. Talbott
Rose-Hulman Undergraduate Mathematics Journal
Serre showed that, for a discrete valuation field, the group of linear fractional transformations acts on an infinite regular tree with vertex degree determined by the residue degree of the field. Since the p-adics and the polynomials over the finite field of order p act on isomorphic trees, we may ask whether pairs of actions from these two groups are ever conjugate as tree automorphisms. We analyze permutations induced on finite vertex sets, and show a permutation classification result for actions by these linear fractional transformation groups. We prove that actions by specific subgroups of these groups are conjugate only …
New Experimental Investigations For The 3𝑥+1 Problem: The Binary Projection Of The Collatz Map, Benjamin Bairrington, Aaron Okano
New Experimental Investigations For The 3𝑥+1 Problem: The Binary Projection Of The Collatz Map, Benjamin Bairrington, Aaron Okano
Rose-Hulman Undergraduate Mathematics Journal
The 3x + 1 Problem, or the Collatz Conjecture, was originally developed in the early 1930's. It has remained unsolved for over eighty years. Throughout its history, traditional methods of mathematical problem solving have only succeeded in proving heuristic properties of the mapping. Because the problem has proven to be so difficult to solve, many think it might be undecidable. In this paper we brie y follow the history of the 3x + 1 problem from its creation in the 1930's to the modern day. Its history is tied into the development of the Cosper Algorithm, which maps binary sequences …