Related papers: Non-recurrent parameter rays of the Mandelbrot set
In a right-angle crossing (RAC) drawing of a graph, each edge is represented as a polyline and edge crossings must occur at an angle of exactly $90^\circ$, where the number of bends on such polylines is typically restricted in some way.…
Phase delays, spectral, orientation, and angular dependences of radiation refraction in metamaterial targets have been experimentally studied within the millimeter-wave range. It has been shown that angular and spectral dependences have a…
It is shown that a non-relativistic Fermi particle with a non-zero rest energy moving in a pseudoscalar ${\delta}$-function potential in one dimension can be confined for both signs of the coupling constant. The binding energies depend on…
The existence of non-continuous invariant graphs (or strange non-chaotic attractors) in quasiperiodically forced systems has generated great interest, but there are still very few rigorous results about the properties of these objects. In…
A continuum theory is employed to numerically study the equilibrium orientation and defect structures of a circular cylindrical particle with flat ends under a homeotropic anchoring condition in a uniform nematic medium. Different aspect…
Recently, conservative extensions of Peano and Heyting arithmetic in the spirit of Nelson's axiomatic approach to Nonstandard Analysis, have been proposed. In this paper, we study the Transfer axiom of Nonstandard Analysis restricted to…
We suggest a new type of the undulator radiation which is generated by an ultra-relativistic particle channeled along a periodically bent crystallographic plane or axis. The electromagnetic radiation arises mainly due to the bending of the…
We consider the high frequency Helmholtz equation with a variable refraction index $n^2(x)$ ($x \in \R^d$), supplemented with a given high frequency source term supported near the origin $x=0$. A small absorption parameter…
Convergence to stationary solutions in fully nonlinear parabolic systems with general nonlinear boundary conditions is shown in situations where the set of stationary solutions creates a $C^2$-manifold of finite dimension which is normally…
We are concerned with inverse boundary problems for first order perturbations of the Laplacian, which arise as model operators in the acoustic tomography of a moving fluid. We show that the knowledge of the Dirichlet--to--Neumann map on the…
Impulsive dynamical systems, modeled by a continuous semiflow and an impulse function, may be discontinuous and may have non-intuitive topological properties, as the non-invariance of the non-wandering set or the non-existence of invariant…
We determine the limiting dynamics of a fermionic condensate following a sudden perturbation for various initial conditions. We demonstrate that possible initial states of the condensate fall into two classes. In the first case, the order…
We consider quantum systems with a chaotic classical limit that depend on an external parameter, and study correlations between the spectra at different parameter values. In particular, we consider the parametric spectral form factor…
In this paper we examine necessary conditions for an anisotropic inhomogeneous medium to be non-scattering at a single wave number and for a single incident field. These conditions are expressed in terms of the regularity of the boundary of…
We investigate typical properties of nonexpansive mappings on unbounded complete hyperbolic metric spaces. For two families of metrics of uniform convergence on bounded sets, we show that the typical nonexpansive mapping is a Rakotch…
We consider the multifractal analysis for Birkhoff averages of continuous potentials on a class of non-conformal repellers corresponding to the self-affine limit sets studied by Lalley and Gatzouras. A conditional variational principle is…
In this paper we start a global study of the parameter space (dissipation, perturbation, frequency) of the dissipative spin-orbit problem in Celestial Mechanics with the aim of delimiting regions where the dynamics, or at least some of its…
We propose a novel and systematic recurrence method for the energy spectra of non-Hermitian systems under open boundary conditions based on the recurrence relations of their characteristic polynomials. Our formalism exhibits better accuracy…
We discuss the nonlinear phenomena of irreversible tipping for non-autonomous systems where time-varying inputs correspond to a smooth "parameter shift" from one asymptotic value to another. We express tipping in terms of pullback…
We study parameter families of quasiperiodically forced (qpf) circle maps with Diophantine frequency. Under certain C1-open conditions concerning their geometry, we prove that these families exhibit nonuniformly hyperbolic behaviour, often…