We study periodic infinite billiards in the plane. We show that for rational models, some particular obstacles can be added periodically, so that the billiard flow in the resulting table is recurrent in almost every direction.
We consider general (not necessarily Hamiltonian) perturbations of Hamiltonian systems with one degree of freedom near separatrices of the unperturbed system. We present asymptotic formulas for change of slow variables at evolution across separatrices.
We give a short proof that there exists a countable state Bernoulli measure maximizing the dimension of their images under the continued fraction expansion.
Anna Przybylska, Grzegorz Bazylak, Robert Kosicki
et al.
Patulin (PAT) is a highly genotoxic mycotoxin still found as the common contaminant of various kinds of spoiled fruits and related commodities which are often endorsed as the health-enhancing products. Thus, a fast and convenient liquid-solid extraction followed by a solid-phase cleanup with the MycoSep®228 AflaPat multifunctional column was used for the highly efficient isolation of PAT with an average recovery of 112.7% from commercial dietary supplements and herbal blends formulated with dried hawberry. Analysis of the PAT content was carried out using gradient elution with a Synergi Polar C18 column (150 × 2 mm, 4 μm) and UHPLC system equipped with a mass spectrometer. PAT was detected in all (n=14) commercial single-component dietary supplements formulated with dried hawberry belonging to Crataegus monogyna and/or Crataegus laevigata. Similarly, PAT was detected in 67% of the studied multicomponent commercial herbal blends (n=6) that contained—in addition to hawberry—different amounts of apple, chokeberry, elderberry, hibiscus, or mallow. Moreover, the PAT content was determined in the hawberry collected from the mature wild hawthorn trees belonging to three botanical species, Crataegus monogyna Jacq., Crataegus laevigata (Poiret) DC, and Crataegus rhipidophylla Gand, growing in the recreational forest areas and in the law-protected state national forest park in Poland. In conclusion, to prevent PAT accumulation and reduce the health risk of consumers in globalizing markets, the implementation of improved cultivation/processing practices of hawthorn trees and hawberry as well as increased analytical control related to the presence of PAT in dietary supplements and herbal blends formulated with fresh, dried, or frozen hawberry should be urgently recommended.
We construct a $C^1$ symplectic twist map $g$ of the annulus that has an essential invariant curve $Γ$ such that $Γ$ is not differentiable and $g$ restricted to $Γ$ is minimal.
We prove an infinite-dimensional KAM theorem for a Hamiltonian system with sublinear growth frequencies at infinity. As an application, we prove the reducibility of the linear fractional Schrödinger equation with quasi-periodic time-dependent forcing.
The elements present in dead pine stumps inhabited by larvae of wood-boring beetles (Stictoleptura rubra, Arhopalus rusticus and Chalcophora mariana) were analyzed over the initial (first 5 years; a chronosequence) stages of wood decay. The quantities of N, P, K, Ca, Mg, Fe, Zn, Mn, Cu and Na (but not S) increased with increases in the content of ergosterol (used as a proxy for the amount of fungal tissue). In fact, the amounts of P, N, K, Fe and Cu presented marked increases. These findings show that fungi stoichiometrically rearrange dead wood by importing externally occurring nutrients to decaying stumps. During the first years of wood decay, the ratios of C to other elements decrease substantially, but differently, for various elements, whereas the N:Fe, N:Cu, N:P and N:K ratios remain relatively stable. Therefore, the stoichiometric mismatch between xylophages and their food is greatly reduced. By changing the nutritional stoichiometry of dead wood, fungi create a nutritional niche for wood-eaters, and these changes enable the development of xylophages.
Let $M$ be a closed smooth manifold and let $f:M\to M$ be a diffeomorphism. $C^1$-generically, a continuum-wise expansive satisfies Axiom A without cycles. Moreover, there is a partially hyperbolic diffeomorphism $f$ such that it is not continuum-wise expansive.
Based on the Lie group theory, the one-parameter Lie group admitted by a Silnikov equation is studied. The result reveals that the Silnikov equation accepts no global analytical non-trivial one-parameter Lie group. In this sense, the Silnikov equation is not integrable in quadrature.
For two families of Weierstrass elliptic functions - based on triangular or square lattices - we prove that the set of Misiurewicz parameters has the Lebesgue measure zero in C.
We study subshift that arise by excluding words of length two from Dyck shifts. The words that are to be excluded are taken from a finite set that is not literal-uniform.
A fractal function is a function whose graph is the attractor of an iterated function system. This paper generalizes analytic continuation of an analytic function to continuation of a fractal function.
We show that for a finitely generated group of $C^2$ circle diffeomorphisms, the entropy of the action equals the entropy of the restriction of the action to the non-wandering set.
We study dynamics of a substitution subshift given by the substitution a->aca, b->d, c->b, d->c that is related to the Grigorchuk group. This dynamical system is shown to be, up to a countable set, conjugated to the binary odometer.