Related papers: Five Definitions of Critical Point at Infinity
We show that the variation of the topology at infinity of a two-variable polynomial function is localisable at a finite number of "atypical points" at infinity. We construct an effective algorithm with low complexity in order to detect…
This note will study complex polynomial maps of degree $n\ge 2$ with only one critical point.
The concept of critical points in nuclear phase transitional regions is discussed from the standpoints of Q-invariants, simple observables and wave function entropy. It is shown that these critical points very closely coincide with the…
We study infinite binary words that contain few distinct palindromes. In particular, we classify such words according to their critical exponents. This extends results by Fici and Zamboni [TCS 2013]. Interestingly, the words with 18 and 20…
In this note a definition of umbilic point at infinity is proposed, at least for surfaces that are homogeneous polynomial graphs over a plane in Euclidean 3-space. This is a stronger definition than that of Toponogov in his study of…
We compare and contrast various notions of the "critical locus" of a complex analytic function on a singular space. After choosing a topological variant as our primary notion of the critical locus, we justify our choice by generalizing L\^e…
In this paper, we obtain new results on the critical points of a polynomial. We discuss the Sendov conjecture for polynomials of degree nine.
In this paper, making use of Theorem 2 of [5], we establish a new four critical points theorem which can be regarded as a companion to Theorem 1 of [4]. We also present an application to the Dirichlet problem for a class of quasilinear…
We give the classification, up to homeomorphisms, of reduced complex polynomials with 2 variables with one critical value.
Let f be a real or complex polynomial. We give an algorithm to compute the set of generalized critical values. The algorithm uses a finite dimensional space of rational arcs along which we can reach all generalized critical values of f.
In this article, we study critical points (zeros of derivative) of random polynomials. Take two deterministic sequences $\{a_n\}_{n\geq1}$ and $\{b_n\}_{n\geq1}$ of complex numbers whose limiting empirical measures are same. By choosing…
The critical point degree of a periodic graph operator is the number of critical points of its complex Bloch variety. Determining it is a step towards the spectral edges conjecture and more generally understanding Bloch varieties. Previous…
It is shown that a polynomial with a Cremer periodic point has a non-accessible critical point in its Julia set provided that the Cremer periodic point is approximated by small cycles.
We prove new multiplicity results for some elliptic problems with critical exponential growth. More specifically, we show that the problems considered here have arbitrarily many solutions for all sufficiently large values of a certain…
We study infinite ternary words that contain few distinct palindromes. In particular, we classify such words according to their critical exponent.
This is the first in a series of three papers where we study the integral manifolds of the charged three-body problem. The integral manifolds are the fibers of the map of integrals. Their topological type may change at critical values of…
The critical point between varieties A and B of algebras is defined as the least cardinality of the semilattice of compact congruences of a member of A but of no member of B, if it exists. The study of critical points gives rise to a whole…
There is shown how to compute the sum of indices of critical points of rank two for polynomial selmaps of R^4
In this paper we study the fractional analogue of the Allen-Cahn energy in bounded domains, and we show that it admits a number of critical points which goes to infinity as the perturbation parameter tends to zero.
In this paper we study an index of a critical orbit, defined in terms of the degree for invariant strongly indefinite functionals. We establish a relationship of this index with the index of a critical point of the mapping restricted to the…