On the pointwise dimension of hyperbolic measures: a proof of the Eckmann-Ruelle conjecture.
On the positivity of an invariant measure on open non-empty sets
On the prescribed-period problem for autonomous Hamiltonian systems.
On the preservation of combinatorial types for maps on trees
We study the preservation of the periodic orbits of an -monotone tree map in the class of all tree maps having a cycle with the same pattern as . We prove that there is a period-preserving injective map from the set of (almost all) periodic orbits of into the set of periodic orbits of each map in the class. Moreover, the relative positions of the corresponding orbits in the trees and (which need not be homeomorphic) are essentially preserved.
On the primary orbits of star maps (first part)
This paper is the first one of a series of two, in which we characterize a class of primary orbits of self maps of the 4-star with the branching point fixed. This class of orbits plays, for such maps, the same role as the directed primary orbits of self maps of the 3-star with the branching point fixed. Some of the primary orbits (namely, those having at most one coloured arrow) are characterized at once for the general case of n-star maps.
On the primary orbits of star maps (second part: spiral orbits)
This paper is the second part of [2] and is devoted to the study of the spiral orbits of self maps of the 4-star with the branching point fixed, completing the characterization of the strongly directed primary orbits for such maps.
On the principle of stability of invariance of physical systems
On the Principle of Stationary Isoenergetic Action
On the problem of stability for near to integrable Hamiltonian systems.
On the ∗-product in kneading theory
We discuss a generalization of the *-product in kneading theory to maps with an arbitrary finite number of turning points. This is based on an investigation of the factorization of permutations into products of permutations with some special properties relevant for dynamics on the unit interval.
On the quasiconformal surgery of rational functions
On the question of stability in a Hamiltonian system
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