Related papers: Lattes maps on P^2

This paper is a continuation of an earlier one, and completes a classification of the configurations of points in a plane lattice that determine angles that are rational multiples of ${\pi}$. We give a complete and explicit description of…

In this paper we study the classification problem of convex lattice ploytopes with respect to given volume or given cardinality.

We proved that the solutions of $C^2$ class of certain ODEs or PDEs belong to a class of harmonic maps between two convenient generalized Lagrange spaces.

We introduce a functional Lebesgue classification of multivalued mappings and obtain results on upper and lower Lebesgue classifications of multivalued mappings $F:X\times Y\to Z$ for wide classes of spaces $X$, $Y$ and $Z$.

This is a survey of results in the enumeration of lattice paths.

We prove that the classification problem for graphs and several types of algebraic lattices (distributive, congruence and modular) up to isomorphism contains the classification problem for pairs of matrices up to simultaneous similarity.

We introduce the notion of the second lattice width of a lattice polytope and use this to classify lattice triangles by their width and second width. This is equivalent to classifying lattice triangles contained in a given rectangle (and no…

This paper is devoted to the description of complex finite-dimensional algebras of level two. We obtain the classification of algebras of level two in the varieties of Jordan, Lie and associative algebras.

We present several characterizations of circle graphs, which follow from Bouchet's circle graph obstructions theorem.

We review the method developed in Pisa to determine the topological susceptibility in lattice QCD and present a collection of new and old results obtained by the method.

This is an expanded version of our work [AN88], 1988, in Russian. We classify del Pezzo surfaces over C with log terminal singularities of index \le 2. By classification, we understand a description of the intersection graph of all…

We classify all $\pi_1$-injective proper maps between non-compact surfaces up to proper homotopy.

We prove that any Latt\`es map can be approximated by strictly postcritically finite rational maps which are not Latt\`es maps.

We consider posets of lattice paths (endowed with a natural order) and begin the study of such structures. We give an algebraic condition to recognize which ones of these posets are lattices. Next we study the class of Dyck lattices (i.e.,…

We determine (multi)graded Betti numbers of path ideals of lines and star graphs.

For a Latt\`es map $\phi:\mathbb P^1 \to \mathbb P^1$ defined over a number field $K$, we prove a conjecture on the integrality of points in the backward orbit of $P\in \mathbb P^1(\overline K)$ under $\phi$.

For an arbitrary partially ordered set $P$ its {\em dual} $P^*$ is built as the collection of all monotone mappings $P\to\2$ where $\2=\{0,1\}$ with $0<1$. The set of mappings $P^*$ is proved to be a complete lattice with respect to the…

We show the existence of open sets of bifurcations near Latt{\`e}s maps of sufficiently high degree. In particular, every Latt{\`e}s map has an iterate which is in the closure of the interior of the bifurcation locus. To show this, we…

We investigate the separability of several well known classes of subgroups of the mapping class group of a surface.

We classify unital associative conformal algebras of linear growth and provide new examples of such.