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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Coexistence of nonempty Fatou sets and Julia sets with interior for transcendental Hénon maps
超Hénon映射 非空Fatou集 Julia集 内部共存性
2023/11/29
A Hénon map is a map of the form H(z, w) = (f(z) + aw, z). A main focus of interest are the Fatou sets and the Julia sets. In this lecture I will show that it is possible that the Fatou set and the Ju...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：On the Gauss maps of complete minimal surfaces in Rm
Rm 完全极小曲面 高斯映射
2023/12/11
We prove that if the Gauss map of a minimal surface immersed in Rm omits a generic hypersurface of large enough degree, then it must be constant.
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Bounded Poincaré maps for BGG complexes
BGG复形 有界 Poincaré映射
2023/5/10
Poincaré integral operators give explicit potential and provide an inverse of differential operators in the sense of null-homotopy. These operators play a key role in the mathematical and numerical an...
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 ...
Harmonic Maps and Teichmuller Theory
Teichmuller space harmonic maps Weil-Petersson metric mapping class group character variety Higgs bundle
2015/12/17
Teichmuller theory is rich in applications to topology and physics. By way of the mapping class group the subject is closely related to knot theory and threemanifolds. From the uniformization theorem,...
Energy of Harmonic Maps and Gardiner’s Formula
Harmonic maps Teichmuller space measured foliation
2015/12/17
It is shown that the usual first variational formula for the energy of a harmonic map (or equivariant harmonic map) with respect to the conformal structure on a two dimensional domain extends to case ...
A block code from an irreducible shift of finite type can be lifted canonically through resolving maps to a resolving map. There is an application to Markovian maps.
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...
Random Iteration of Maps on a Cylinder and diffusive behavior
Random Iteration of Maps Cylinder diffusive
2015/9/25
Random Iteration of Maps on a Cylinder and diffusive behavior.
NEW EXAMPLES OF S-UNIMODAL MAPS WITH A SIGMA-FINITE ABSOLUTELY CONTINUOUS INVARIANT MEASURE
S-UNIMODAL MAPS SIGMA-FINITE ABSOLUTELY CONTINUOUS INVARIANT MEASURE
2015/9/25
We combine the technique of inducing with a method of Johnson boxes and construct new examples of S-unimodal maps ϕ which do not have a finite absolutely continuous invariant measure, but do have...
NEW EXAMPLES OF TOPOLOGICALLY EQUIVALENT S-UNIMODAL MAPS WITH DIFFERENT METRIC PROPERTIES
TOPOLOGICALLY EQUIVALENT S-UNIMODAL MAPS DIFFERENT METRIC PROPERTIES
2015/9/25
We construct examples of topologically conjugate unimodal maps, such that both of them have an absolutely continuous invariant measure, but for one of them that measure is finite, and for another one ...
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...
We construct a hyperbolic group with a hyperbolic subgroup for which inclusion does not induce a map of the boundaries.
The Classificationof Topologically Expansive Lorenz Maps
Classificationof Topologically Expansive Lorenz Maps
2015/8/26
We show that topologically expansive Lorenz maps can be described up to topological conjugacy by their kneading invariants. We also give a simple condition on pairs of symbol sequences which is satisf...