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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...
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.
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...
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 ...
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,...
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.
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...
Random Iteration of Maps on a Cylinder and diffusive behavior.
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...
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 ...
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.
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...

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