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ENERGY OF TWISTED HARMONIC MAPS OF RIEMANN SURFACES
Riemann surface fundamental group flat bundle harmonic map energy Teichmuller space convex cocompact hyperbolic manifold
2015/12/17
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 ...
THE DIFFUSION COEFFICIENT FOR PIECEWISE EXPANDING MAPS OF THE INTERVAL WITH METASTABLE STATES
DIFFUSION COEFFICIENT WITH METASTABLE STATES
2015/9/29
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).
REGULARITY OF ABSOLUTELY CONTINUOUS INVARIANT MEASURES FOR PIECEWISE EXPANDING UNIMODAL MAPS
INVARIANT MEASURES UNIMODAL MAPS
2015/9/29
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...
PARAMETER CHOICE FOR FAMILIES OF MAPS WITH MANY CRITICAL POINTS
PARAMETER CHOICE MAPS WITH MANY CRITICAL POINTS
2015/9/25
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...
Quantitative Stratification and the Regularity of Harmonic Maps and Minimal Currents
Quantitative Stratification the Regularity of Harmonic Maps Minimal Currents
2011/9/9
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...
On affine maps on non-compact convex sets and some characterizations of finite-dimensional solid ellipsoids
affine maps non-compact convex sets characterizations of finite-dimensional solid ellipsoids
2011/2/25
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...
Logarithmic tensor category theory, III: Intertwining maps and tensor product bifunctors
Logarithmic tensor category theory Intertwining maps and tensor product bifunctors
2011/2/23
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 (...
Biharmonic Riemannian maps
Riemannian map pseudo umbilical Riemannian map harmonic map biharmonic
2011/1/20
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...
Period Doubling Renormalization for Area-Preserving Maps and Mild Computer Assistance in Contraction Mapping Principle
Period Doubling Renormalization Area-Preserving Maps Mild Computer Assistance
2010/11/29
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 ...
Gauss maps of constant mean curvature surfaces in three-dimensional homogeneous spaces
Gauss maps of constant mean curvature surfaces three-dimensional homogeneous spaces
2010/11/26
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...
Mixed Non-Expansive and Potentially Expansive Properties of a Class of Self-Maps in Metric Spaces
contractive maps non-expansive maps metric space fixed points
2010/12/15
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...