167 citations · 519 across the 84 of their papers we have counts for
8 papers · 1 filter
Interleaving of path sets
William C. Abram, Jeffrey C. Lagarias, Daniel Slonim
Path sets are spaces of one-sided infinite symbol sequences corresponding to the one-sided infinite walks beginning at a fixed initial vertex in a directed labeled graph. Path sets…
Decimation and Interleaving Operations in One-Sided Symbolic Dynamics
William C. Abram, Jeffrey C. Lagarias, Daniel J. Slonim
This paper studies subsets of one-sided shift spaces on a finite alphabet. Such subsets arise in symbolic dynamics, in fractal constructions, and in number theory. We study a famil…
Path sets in one-sided symbolic dynamics
William Abram, Jeffrey C. Lagarias
Path sets are spaces of one-sided infinite symbol sequences associated to pointed graphs (G_v_0), which are edge-labeled directed graphs G with a distinguished vertex v_0. Such set…
Ternary expansions of powers of 2
Jeffrey C. Lagarias
Paul Erdos asked how frequently the ternary expansion of 2^n omits the digit 2. He conjectured this happens only for finitely many values of n. We generalize this question to consi…
Dynamics of a family of piecewise-linear area-preserving plane maps III. Cantor set spectra
Jeffrey C. Lagarias, Eric Rains
This paper studies the behavior under iteration of the maps T_{ab}(x,y) = (F_{ab}(x)- y, x) of the plane R^2, in which F_{ab}(x)= ax if x>0 and bx if x<0. These maps are area-prese…
Dynamics of a family of piecewise-linear area-preserving plane maps II. Invariant circles
Jeffrey C. Lagarias, Eric M. Rains
This paper studies the behavior under iteration of the maps T_{ab}(x,y)=(F_{ab}(x)-y,x) of the plane R^2, in which F_{ab}(x)=ax if x>=0 and bx if x<0. The orbits under iteration co…