In dynamical systems, the invariant tori named for Kolmogorov, Arnold, and Moser which not destroyed by perturbation become this invariant construct. The paths in an infinite complete binary tree correspond to an order-preserving bijection to this construct. Smith, Volterra, and its namesake formulated a "fat" version of this construct which has positive measure, while the original has zero measure. This construct is a totally disconnected space, and is a fractal with dimension log base three of two. The (*) Sierpinski carpet and Menger sponge are the two- and three-dimensional generalizations of this construct, while a finite Cartesian product generates its namesake multi-dimensional "dust." It is constructed by deleting the open middle thirds of a set of line segments ad infinitum. For 10 points, what is this se
In dynamical systems, the invariant tori named for Kolmogorov, Arnold, and Moser which not destroyed by perturbation become this invariant construct. The paths in an infinite complete binary tree correspond to an order-preserving bijection to this construct. Smith, Volterra, and its namesake formulated a "fat" version of this construct which has positive measure, while the original has zero measure. This construct is a totally disconnected space, and is a fractal with dimension log base three of two. The (*) Sierpinski carpet and Menger sponge are the two- and three-dimensional generalizations of this construct, while a finite Cartesian product generates its namesake multi-dimensional "dust." It is constructed by deleting the open middle thirds of a set of line segments ad infinitum. For 10 points, what is this set discovered by the man with a namesake "diagonal argument?"
In dynamical systems, the invariant tori named for Kolmogorov, Arnold, and Moser which not destroyed by perturbation become this invariant construct.
Cantor set