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The energy of harmonic sections of flat bundles of nonpositively curved (NPC) length spaces over a Riemann surface S is a function E ρ on Teichm¨uller space TS which is a qualitative invariant of the ...
Consider a piecewise smooth expanding map of the interval possessing several invariant subintervals and the same number of ergodic absolutely continuous invariant probability measures (ACIMs).
An important discovery of the 20th century mathematics is that many deterministic systems exhibit stochastic behavior. The stochasticity is caused by exponential divergence of nearby trajectories. Th...
We consider families of smooth one-dimensional maps with several critical points and outline the main ideas of the construction in the parameter space that allows to get infinite Markov Partitions and...
Abstract: We introduce techniques for turning estimates on the infinitesimal behavior of solutions to nonlinear equations (statements concerning tangent cones and blow ups) into more effective control...
Abstract: This is a pedagogical introduction covering maps of metric spaces, Gromov-Hausdorff distance and its "physical" meaning, and dilation structures as a convenient simplification of an exhausti...
In recent studies, properties of the set of affine maps between two convex sets have been investigated with intensive motivation from quantum physics, but in those preceding works the underlying con...
This is the third part in a series of papers in which we introduce and develop a natural, general tensor category theory for suitable module categories for a vertex (operator) algebra. In this paper (...
We give necessary and sufficient conditions for Riemannian maps to be biharmonic. We also define pseudo umbilical Riemannian maps as a generalization of pseudo-umbilical submanifolds and show that suc...
Our main result states that every fixed-point free continuous self-map of ${\mathbb R}^{n}$ is colorable. This result can be re-formulated as follows: A continuous map $f: {\mathbb R}^{n}\to {\mathbb...
In previous work, a class of noninvertible topological dynamical systems $f: X \to X$ was introduced and studied; we called these {\em topologically coarse expanding conformal} systems. To such a sys...
We describe work on solutions of certain non-divergence type and therefore non-variational elliptic and parabolic systems on manifolds. These systems include Hermitian and affine harmonics which shou...
A universal period doubling cascade analogous to the famous Feigenbaum-Coullet-Tresser period doubling has been observed in area-preserving maps of R2. Existence of the “universal” map with orbits of ...
It is well-known that for a surface in a 3-dimensional real space form the constancy of the mean curvature is equivalent to the harmonicity of the Gauss map. However, this is not true in general for...
This paper investigates self-maps T : X  X which satisfy a distance constraint in a metric space which mixed point-dependent non-expansive properties, or in particular contractive ones, and p...

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