Stable and non-stable non-chaotic maps of the interval
Stable closed orbits in plane autonomous dynamical systems.
Stable ergodicity and julienne quasi-conformality
In this paper we dramatically expand the domain of known stably ergodic, partially hyperbolic dynamical systems. For example, all partially hyperbolic affine diffeomorphisms of compact homogeneous spaces which have the accessibility property are stably ergodic. Our main tools are the new concepts – julienne density point and julienne quasi-conformality of the stable and unstable holonomy maps. Julienne quasi-conformal holonomy maps preserve all julienne density points.
Stable ergodicity of skew products
Stable global attractors in
Stable intersections of Cantor sets and homoclinic bifurcations
Stable norms of non-orientable surfaces
We study the stable norm on the first homology of a closed non-orientable surface equipped with a Riemannian metric. We prove that in every conformal class there exists a metric whose stable norm is polyhedral. Furthermore the stable norm is never strictly convex if the first Betti number of the surface is greater than two.
Stable planar polynomial vector fields.
Stable rank and real rank of compact transformation group C*-algebras
Let (G,X) be a transformation group, where X is a locally compact Hausdorff space and G is a compact group. We investigate the stable rank and the real rank of the transformation group C*-algebra C₀(X)⋊ G. Explicit formulae are given in the case where X and G are second countable and X is locally of finite G-orbit type. As a consequence, we calculate the ranks of the group C*-algebra C*(ℝⁿ ⋊ G), where G is a connected closed subgroup of SO(n) acting on ℝⁿ by rotation.
Stage-structured impulsive model for pest management.
Staircase baker's map generates flaring-type time series.
Stalking staggeringly large numbers
Star-products on symplectic manifolds
Stastistic of the winding of geodesics on a Riemann surface with finite area and constant negative curvature.
In this paper we show that the windings of geodesics around the cusps of a Riemann surface of a finite area, behave asymptotically as independent Cauchy variables.
Statistical analysis of time series with scaling indices.
Statistical periodicity of deterministic systems
Statistical properties of Markov dynamical sources: applications to information theory.
Statistical properties of topological Collet–Eckmann maps
Statistical properties of unimodal maps
We consider typical analytic unimodal maps which possess a chaotic attractor. Our main result is an explicit combinatorial formula for the exponents of periodic orbits. Since the exponents of periodic orbits form a complete set of smooth invariants, the smooth structure is completely determined by purely topological data (“typical rigidity”), which is quite unexpected in this setting. It implies in particular that the lamination structure of spaces of analytic unimodal maps (obtained by the partition...
Statistical stability of geometric Lorenz attractors
We consider the robust family of geometric Lorenz attractors. These attractors are chaotic, in the sense that they are transitive and have sensitive dependence on initial conditions. Moreover, they support SRB measures whose ergodic basins cover a full Lebesgue measure subset of points in the topological basin of attraction. Here we prove that the SRB measures depend continuously on the dynamics in the weak* topology.