Generalizing the arithmetic geometric mean - a hapless computer experiment.
Geometric and arithmetic properties of the Hénon map.
Harmonic, Gibbs and Hausdorff measures on repellers for holomorphic maps, II
Hausdorff dimension for piecewise monotonic maps
How complicated can be one-dimensional dynamical systems: descriptive estimates of sets
Implicit Differential Equations From the Singularity Theory Viewpoint
Infinite Iterated Function Systems: A Multivalued Approach
We prove that a compact family of bounded condensing multifunctions has bounded condensing set-theoretic union. Compactness is understood in the sense of the Chebyshev uniform semimetric induced by the Hausdorff distance and condensity is taken w.r.t. the Hausdorff measure of noncompactness. As a tool, we present an estimate for the measure of an infinite union. Then we apply our result to infinite iterated function systems.
Invariant curves from symmetry
We show that certain symmetries of maps imply the existence of their invariant curves.
Inverse limits of certain interval mappings as attractors in two dimensions
Iteration of a quaternionic quadratic family.
Iterations of rational functions: which hyperbolic components contain polynomials?
Let be the set of all rational maps of degree d ≥ 2 on the Riemann sphere, expanding on their Julia set. We prove that if and all, or all but one, critical points (or values) are in the basin of immediate attraction to an attracting fixed point then there exists a polynomial in the component H(f) of containing f. If all critical points are in the basin of immediate attraction to an attracting fixed point or a parabolic fixed point then f restricted to the Julia set is conjugate to the shift...
Links of homeomorphisms of a disk and topological entropy.
Mapping properties of Fatou components.
Maps of the interval Ljapunov stable on the set of nonwandering points.
Maximal scrambled sets for simple chaotic functions.
This paper is a continuation of [1], where a explicit description of the scrambled sets of weakly unimodal functions of type 2∞ was given. Its aim is to show that, for an appropriate non-trivial subset of the above family of functions, this description can be made in a much more effective and informative way.
Multifractal analysis of nearly circular Julia set and thermodynamical formalism
Multimodal cycles with linear map having exactly one fixed point.
Nilsystèmes d’ordre 2 et parallélépipèdes
En topologie dynamique, une famille classique de systèmes est celle formée par les rotations minimales. La classe des nilsystèmes et de leurs limites projectives en est une extension naturelle. L’étude de ces systèmes est ancienne mais connaît actuellement un renouveau à cause de ses applications, à la fois à la théorie ergodique et en théorie additive des nombres. Les rotations minimales sont caractérisées par le fait que la relation de proximalité régionale est l’égalité. Nous introduisons une...
Noether theorem and first integrals of constrained Lagrangean systems
The dynamics of singular Lagrangean systems is described by a distribution the rank of which is greater than one and may be non-constant. Consequently, these systems possess two kinds of conserved functions, namely, functions which are constant along extremals (constants of the motion), and functions which are constant on integral manifolds of the corresponding distribution (first integrals). It is known that with the help of the (First) Noether theorem one gets constants of the motion. In this...
Nonarchimedean dynamical systems