This book is based on a course given at the University of Chicago in 1980-81. As with the
course, the main motivation of this work is to present an accessible treatment, assuming …

Let G be a connected Lie group and Γ be a lattice in G; that is, Γ is a discrete subgroup of G
such that G/Γ admits a finite G-invariant measure. Let {gt} teP be a oneparameter subgroup …

The class of all invariant measures of a transformation, or a flow, is an important aspect of its
dynamics. Thus for instance if T is a homeomorphism of a locally compact space X then any …

Let L be a Lie group and λ a lattice in L. Suppose G is a non-compact simple Lie group
realized as a Lie subgroup of L and GA= L. Let aεG be such that Ada is semisimple and not …

Publisher Summary This chapter presents an exposition of homogeneous dynamics—that is,
the dynamical and ergodic properties of actions on the homogeneous spaces of Lie groups …

We show that if (ut) is a one-parameter subgroup of SL (n, ℝ) consisting of unipotent
matrices, then for any ε> 0 there exists a compact subset K of SL (n, ℝ)/SL (n, ℤ) such that …

Kolmogorov–Arnold–Moser (or KAM) Theory was developed for conservative (Hamiltonian)
dynamical systems that are nearly integrable. Integrable systems in their phase space …

We consider perturbations of moderately degenerate integrable or partially integrable
Hamiltonian systems, so that unperturbed invariant n-tori with prescribed frequencies or …

We consider a subgroup Γ of the linear group G= Sl (d, ℝ), the unipotent subgroup N of
upper triangular matrices and the subgroup A of positive diagonal matrices. The subgroup Γ …

Let G be a Lie group and C be a closed subgroup of G. The quotient G/C is also called a
homogeneous space. To each a Є G corresponds a translation Ta given by xC→ axC. More …