Related papers: Non-recurrent parameter rays of the Mandelbrot set

We complete a full classification of non-degenerate traveling waves of scalar balance laws from the point of view of spectral and nonlinear stability/instability under (piecewise) smooth perturbations. A striking feature of our analysis is…

If $f:[a,b]\to \mathbb{R}$, with $a<b$, is continuous and such that $a$ and $b$ are mapped in opposite directions by $f$, then $f$ has a fixed point in $I$. Suppose that $f:\mathbb{C}\to\mathbb{C}$ is map and $X$ is a continuum. We extend…

The main goal of this paper is the study of two kinds of nonlinear problems depending on parameters in unbounded domains. Using a nonstandard variational approach, we first prove the existence of bounded solutions for nonlinear eigenvalue…

We study the parameter space of unicritical polynomials $f_c:z\mapsto z^d+c$. For complex parameters, we prove that for Lebesgue almost every $c$, the map $f_c$ is either hyperbolic or infinitely renormalizable. For real parameters, we…

We show that non-reciprocal bands can be formed in a magnetized periodic chain of spherical plasmonic particles with two particles per unit cell. Simplified form of symmetry operators in dipole approximations are used to demonstrate…

Determining the symmetry of the order parameter of unconventional superconductors remains a recurrent topic and non-trivial task in the field of strongly correlated electron systems. Here we show that the behavior of Dirac points away from…

We consider the problem of asymptotic reconstruction of the state and parameter values in systems of ordinary differential equations. A solution to this problem is proposed for a class of systems of which the unknowns are allowed to be…

Let f be a degree d polynomial defined over the nonarchimedean field C_p, normalized so f is monic and f(0)=0. We say f is post-critically bounded, or PCB, if all of its critical points have bounded orbit under iteration of f. It is known…

In this paper we present criteria for the choice of the shape parameter c contained in the famous radial function multiquadric. It may be of interest to RBF people and all people using radial basis functions to do approximation.

Standard bifurcation theory is concerned with families of vector fields $dx/dt = f(x,\lambda)$, $x \in \R^n$, involving one or several constant real parameters $\lambda$. Viewed as a differential equation for the pair $(x,\lambda)$, we…

In this article we study the Arnold conjecture in settings where objects under consideration are no longer smooth but only continuous. The example of a Hamiltonian homeomorphism, on any closed symplectic manifold of dimension greater than…

Using Lavaurs maps and near-parabolic renormalization, we describe the degenerating geometry of external rays for quadratic polynomials when a periodic cycle becomes parabolic. We similarly describe the geometry of parameter rays for the…

This paper is devoted to the investigation of the spectral theory and dynamical properties of periodic graphs which are not locally finite but carry non-negative, symmetric and summable edge weights. These graphs are shown to exhibit rather…

A natural parametrization of smooth projective plane curves which tolerates the presence of sextactic points is the Forsyth-Laguerre parametrization. On a closed projective plane curve, which necessarily contains sextactic points, this…

Let $(R, \mathfrak{m}, k)$ be an excellent equidimensional local ring of characteristic $p>0$. The aim of this paper is to show that $\ell_R(\mathfrak{q}^*/\mathfrak{q})$ does not depend on the choice of parameter ideal $\mathfrak{q}$…

Consider the one-parameter family of cubic polynomials defined by $f_t(z) =-\frac 32 t(-2z^3+3z^2)+1, t \in \mathbb{C}_2$. This family corresponds to a slice of the parameter space of cubic polynomials in $\mathbb{C}_2[z]$. We investigate…

In the present paper we investigate the transmission and reflection band behavior for a plane electromagnetic wave falling obliquely on an ideal layered structure. The dependence of this behavior on the problem parameters and wave incident…

Considering random noise in finite dimensional parameterized families of diffeomorphisms of a compact finite dimensional boundaryless manifold M, we show the existence of time averages for almost every orbit of each point of M, imposing…

We calculate the static critical behavior of systems of $O(n_\|)\oplus O(n_\perp)$ symmetry by renormalization group method within the minimal subtraction scheme in two loop order. Summation methods lead to fixed points describing…

The scattering formulation of characteristic mode decomposition is utilized to extend modal analysis to lossless scatterers breaking time-reversal symmetry. This enables characteristic modes analysis on devices containing gyrotropic or…