Related papers: The size of quadratic $p$-adic linearization disks
In this paper, we find the radius of the disk $\Omega _{r}$ such that every starlike logharmonic mapping $f(z)$ of order $\alpha ,$ is starlike in $% |z|\leq r$ with respect to any point of $\Omega _{r}.$ We also establish a relation…
A large class of flat axially symmetric solutions to the Vlasov-Poisson system is constructed with the property that the corresponding rotation curves are approximately flat, slightly decreasing or slightly increasing. The rotation curves…
In this paper we study the existence and regularity of stable manifolds associated to fixed points of parabolic type in the differentiable and analytic cases, using the parametrization method. The parametrization method relies on a suitable…
Let X be a non-singular projective hypersurface of degree 4, which is defined over the rational numbers. Assume that X has dimension 39 or more, and that X contains a real point and p-adic points for every prime p. Then X is shown to…
In this paper, we introduce the concept of central periodic points of a linear system as points which lies on orbits starting and ending at the central subgroup of the system. We show that this set is bounded if and only if the central…
It is proved that for every complex quadratic polynomial $f$ with Cremer's fixed point $z_0$ (or periodic orbit) for every $\delta>0$, there is at most one periodic orbit of minimal period $n$ for all $n$ large enough, entirely in the disc…
We obtain stochastic stability of C2 non-uniformly expanding one-dimensional endomorphisms, requiring only that the first hyperbolic time map be L^{p}-integrable for p>3. We show that, under this condition (which depends only on the…
If an appropriate region of Kerr-Newman space-time is removed and suitable identifications are made, the resulting space-time can be interpreted as an infinitely thin disk producing the original electromagnetic and gravitational fields. We…
A rational number is dyadic if it has a finite binary representation $p/2^k$, where $p$ is an integer and $k$ is a nonnegative integer. Dyadic rationals are important for numerical computations because they have an exact representation in…
We prove that the space of contractible simple loops of a given fixed area in any compact oriented surface has infinite diameter as a homogeneous space of the group of area-preserving diffeomorphisms endowed with the $L^p$-metric. As a…
We study the dynamics of continuous maps on compact metric spaces containing a free interval (an open subset homeomorphic to the interval $(0,1)$). We provide a new proof of a result of M. Dirb\'ak, \v{L}. Snoha, V. \v{S}pitalsk\'y [Ergodic…
We present the first local simulations of disc breaking/tearing in a warped accretion disc. Warps can arise due to a misalignment between the disc and the rotation axis of the central object, or a misalignment with the orbital plane of a…
We extend Sullivan's complex a priori bounds to real quadratic polynomials with essentially bounded combinatorics. Combined with the previous results of the first author, this yields complex bounds for all real quadratics. Local…
Accretion discs that are tilted with respect to their compact hosts can warp out-of-plane through general relativistic frame-dragging. Warp influences disc dynamics in ways that have been studied extensively, especially as regards…
We prove the existence of rational maps having smooth degenerate Herman rings. This answers a question of Eremenko affirmatively. The proof is based on the construction of smooth Siegel disks by Avila, Buff and Ch\'{e}ritat as well as the…
We show that, for planar point sets, the number of non-crossing Hamiltonian paths is polynomially bounded in the number of non-crossing paths, and the number of non-crossing Hamiltonian cycles (polygonalizations) is polynomially bounded in…
We examine the evolution of the Parker instability in galactic disks using 3D numerical simulations. We consider a local Cartesian box section of a galactic disk, where gas, magnetic fields and cosmic rays are all initially in a…
Caustics are curves with the property that a billiard trajectory, once tangent to it, stays tangent after every reflection at the boundary of the billiard table. When the billiard table is an ellipse, any nonsingular billiard trajectory has…
In this article, we continue our investigations of the boundary behavior of harmonic mappings. We first discuss the classical problem on the growth of radial length and obtain a sharp growth theorem of the radial length of…
We show how a certain limit of the nonsymmetric Macdonald polynomials appears in the representation theory of semisimple groups over p--adic fields as matrix coefficients for the unramified principal series representations. The result is…