On the random character of fundamental constant expansions.
On the range of fractional parts {ξ(p/q)ⁿ}
On the rate of convergence to the neutral attractor of a family of one-dimensional maps
For a family of maps , d ∈ [2,∞], p ∈ [0,1]. we analyze the speed of convergence (including constants) to the globally attracting neutral fixed point p = 0. The study is motivated by a problem in the optimization of routing. The aim of this paper is twofold: (1) to extend the usage of dynamical systems to unexplored areas of algorithms and (2) to provide a toolbox for a precise analysis of the iterates near a non-degenerate neutral fixed point.
On the rate of mixing of Axiom A flows.
On the reduction method versus the stability of ordinary linear differential equations with unknown coefficients.
On the relationship between hyperbolic and cone-hyperbolic structures in metric spaces
We give necessary and sufficient conditions for topological hyperbolicity of a homeomorphism of a metric space, restricted to a given compact invariant set. These conditions are related to the existence of an appropriate finite covering of this set and a corresponding cone-hyperbolic graph-directed iterated function system.
On the rotation sets for non-continuous circle maps.
On the spectral flow and the index theorem for flat vector bundles
On the spectral theory and dynamics of asymptotically hyperbolic manifolds
We present a brief survey of the spectral theory and dynamics of infinite volume asymptotically hyperbolic manifolds. Beginning with their geometry and examples, we proceed to their spectral and scattering theories, dynamics, and the physical description of their quantum and classical mechanics. We conclude with a discussion of recent results, ideas, and conjectures.
On the spectrum of stochastic perturbations of the shift and Julia sets
We extend the Killeen-Taylor study [Nonlinearity 13 (2000)] by investigating in different Banach spaces (,c₀(ℕ),c(ℕ)) the point, continuous and residual spectra of stochastic perturbations of the shift operator associated to the stochastic adding machine in base 2 and in the Fibonacci base. For the base 2, the spectra are connected to the Julia set of a quadratic map. In the Fibonacci case, the spectrum is related to the Julia set of an endomorphism of ℂ².
On the sructure of non-singular iteration groups on the circle.
On the stability of elliptic equilibria.
On the stabilization of internally coupled map lattice systems.
On the statistical properties of ergodic economic systems.
On the structure of covers of sofic shifts.
On the structure of homeomorphisms of the open annulus
Let be a without fixed point lift to the plane of a homeomorphism of the open annulus isotopic to the identity and without wandering point. We show that admits a -invariant dense open set on which it is conjugate to a translation and we study the action of on the compactly connected components of the closed and without interior set .
On the structure of minimal attraction centers of recurrent trajectories of continuous maps of the interval.
On the structure of the space of continuous maps with zero topological entropy
On the structure of the totally ordered set of unimodal cycles.
On the Symplectic Structure of Coadjoint Orbits of (Solvable) Lie Groups and Applications. I.