Related papers: Essential perturbations of polynomial vector field…

We revisit the characterization of \emph{trivial} isochronous centers for planar polynomial Hamiltonian systems in degrees $5$ and $7$ obtained by Braun--Llibre--Mereu, and we formalize two conclusions suggested by their method. First, a…

We study relevant perturbations at the spin quantum Hall critical point using a network model formulation. The model has been previously mapped to classical percolation on a square lattice, and we use the mapping to extract exact analytical…

A general procedure for the calculation of a class of two-loop Feynman diagrams is described. These are two-point functions containing three massive propagators, raised to integer powers, in the denominator, and arbitrary polynomials of the…

Closely following recent ideas of J. Borcea, we discuss various modifications and relaxations of Sendov's conjecture about the location of critical points of a polynomial with complex coefficients. The resulting open problems are formulated…

In the weakened 16th Hilbert's Problem one asks for a bound of the number of limit cycles which appear after a polynomial perturbation of a planar polynomial Hamiltonian vector field. It is known that this number is finite for an individual…

In this work, we study the in-plane oscillations of a finite lattice of particles coupled by linear springs under distributed harmonic excitation. Melnikov-type analysis is applied for the persistence of periodic oscillations of a reduced…

Using the general theory of [10] ( hep-th 9412058 ), quantum Poincar\'e groups (without dilatations) are described and investigated. The description contains a set of numerical parameters which satisfy certain polynomial equations. For most…

We describe some families of differentiable vector fields with the Hopf bifurcation at infinity, without assuming the continuous differentiability. These vector fields have isolated singular points on the plane, and the initial families are…

In this paper we consider an abstract class of quasi-linear para-differential equations on the circle. For each equation in the class we prove the existence of a change of coordinates which conjugates the equation to a diagonal and constant…

For piecewise expanding one-dimensional maps without periodic turning points we prove that isolated eigenvalues of small (random) perturbations of these maps are close to isolated eigenvalues of the unperturbed system. (Here ``eigenvalue''…

We prove a theorem on distortion of cross ratio of four points under the mapping effected by a complex polynomial with restricted critical values. Its corollaries include inequalities involving the absolute value and certain coefficients of…

We consider the Markov process defined by some pseudo-differential operator of the order $1<\alpha<2$ as the process generator. Using a pseudo-gradient operator, that is, the operator defined by the symbol $i\lambda|\lambda|^{\beta-1}$ with…

In this work, we explore an unconventional class of problems in the study of (quantum) critical phenomena, termed ''deep boundary criticality''. Traditionally, critical systems are analyzed with two types of perturbations: those uniformly…

Perturbation theory can be reformulated as dynamical theory. Then a sequence of perturbative approximations is bijective to a trajectory of dynamical system with discrete time, called the approximation cascade. Here we concentrate our…

The influence of time-dependent perturbations on an autonomous Hamiltonian system with an equilibrium of center type is considered. It is assumed that the perturbations decay at infinity in time and vanish at the equilibrium of the…

We study, by means of a topological approach, the forced oscillations of second order functional retarded differential equations subject to periodic perturbations. We consider a delay-type functional dependence involving a gamma probability…

We study the existence and stability of Q-balls in noncanonical scalar field theories, $K(|\Phi|^2,X)$ where $\Phi$ is the complex scalar field and $X$ is the kinetic term. We extend the Vakhitov-Kolokolov stability criterion to K-field…

We investigate the structure of the set of $T$-periodic solutions to periodically perturbed coupled delay differential equations on differentiable manifolds. By using fixed point index and degree-theoretic methods we prove the existence of…

The entropic discriminant is a non-negative polynomial associated to a matrix. It arises in contexts ranging from statistics and linear programming to singularity theory and algebraic geometry. It describes the complex branch locus of the…

In this paper, we study the stability of matrix polynomials under structured perturbations of their coefficients. More precisely, we consider a family of matrix polynomials \[…