Abstract

Hamiltonian systems, possessing an infinite hierarchy of islands-around-islands structure, have sticky sets, sets of all limiting points of islands of stability. A class of symbolic systems, called multipermutative, is introduced to model the dynamics in the sticky (multifractal) sets. Every multipermutative system is shown to consist of a collection of minimal subsystems that are topologically conjugate to adding machines. These subsystems are uniquely ergodic. Sufficient and necessary conditions of topological conjugacy are given. A subclass of sticky sets is constructed for which Hausdorff dimension is found and multifractal decomposition is described.