167 citations · 519 across the 84 of their papers we have counts for
5 papers · 1 filter
Approximate Squaring
J. C. Lagarias, N. J. A. Sloane
We study the ``approximate squaring'' map f(x) := x ceiling(x) and its behavior when iterated. We conjecture that if f is repeatedly applied to a rational number r = l/d > 1 then e…
The 3x+1 problem: An annotated bibliography (1963--1999) (sorted by author)
Jeffrey C. Lagarias
The 3x+ 1 problem concerns iteration of the map on the integers given by T(n) = (3n+1)/2 if n is odd; T(n) = n/2 if n is even. The 3x+1 Conjecture asserts that for every positive i…
Area Inequalities for Embedded Disks Spanning Unknotted Curves
Joel Hass, Jeffrey C. Lagarias, William P. Thurston
We show that a smooth unknotted curve in R^3 satisfies an isoperimetric inequality that bounds the area of an embedded disk spanning the curve in terms of two parameters: the lengt…
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…
Dynamics of a family of piecewise-linear area-preserving plane maps I. Rational rotation numbers
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. The orbits under iteration…