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math.DS2005★ 2 cited
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…
math.DS2003
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…
math.DS2003
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…