Identification of discrete chaotic maps with singular points.
Identifying points of a pseudo-Anosov homeomorphism
We investigate the question, due to S. Smale, of whether a hyperbolic automorphism T of the n-dimensional torus can have a compact invariant subset homeomorphic to a compact manifold of positive dimension, other than a finite union of subtori. In the simplest case such a manifold would be a closed surface. A result of Fathi says that T can sometimes have an invariant subset which is a finite-to-one image of a closed surface under a continuous map which is locally injective except possibly at a finite...
Induced expansion for quadratic polynomials
Inductorless Chua's circuit: experimental time series analysis.
Infinitely many coexisting strange attractors
Infinitesimal conjugacies and Weil-Petersson metric
We study deformations of compact Riemannian manifolds of negative curvature. We give an equation for the infinitesimal conjugacy between geodesic flows. This in turn allows us to compute derivatives of intersection of metrics. As a consequence we obtain a proof of a theorem of Wolpert.
Inflationary tilings with a similarity structure.
Informal remarks on the orbit structure of discrete approximations to chaotic maps.
Integrable smooth planar billiards and evolutes.
Invariant densities for C¹ maps
We consider the set of expanding maps of the circle which have a unique absolutely continuous invariant probability measure whose density is unbounded, and show that this set is dense in the space of expanding maps with the topology. This is in contrast with results for or maps, where the invariant densities can be shown to be continuous.
Invariant graphs of functions for the mean-type mappings
Let I be a real interval, J a subinterval of I, p ≥ 2 an integer number, and M1, ... , Mp : Ip → I the continuous means. We consider the problem of invariance of the graphs of functions ϕ : Jp−1 → I with respect to the mean-type mapping M = (M1, ... , Mp).Applying a result on the existence and uniqueness of an M -invariant mean [7], we prove that if the graph of a continuous function ϕ : Jp−1 → I ...
Invariant jets of a smooth dynamical system
The local deformations of a submanifold under the effect of a smooth dynamical system are studied with the help of Oseledets’ multiplicative ergodic theorem. Equivalence classes of submanifolds, called jets, are introduced in order to describe these local deformations. They identify submanifolds having the same approximations up to some order at a given point. For every order , a condition on the Lyapunov exponents of the dynamical system is established insuring the convergence of the -jet of...
Invariant manifolds and cluster synchronization in a family of locally coupled map lattices.
Invariant manifolds associated to invariant subspaces without invariant complements: a graph transform approach.
Invariant Measures and Minimal Sets of Horospherical Flows.
Invariant measures exist under a summability condition for unimodal maps.
Invariant measures for a diffeomorphism which expands the leaves of a foliation
Invariant measures for the stable foliation on negatively curved periodic manifolds
We classify reversible measures for the stable foliation on manifolds which are infinite covers of compact negatively curved manifolds. We extend the known results from hyperbolic surfaces to varying curvature and to all dimensions.
Invariant measures of the geodesic flow and measures at infinity on negatively curved manifolds
Invariant scrambled sets and maximal distributional chaos
For the full shift (Σ₂,σ) on two symbols, we construct an invariant distributionally ϵ-scrambled set for all 0 < ϵ < diam Σ₂ in which each point is transitive, but not weakly almost periodic.