Related papers: On Latt\`es Maps
These notes concern linear transformations on R^n and C^n, exponentials of linear transformations, and some related geometric questions.
High-level Chinese cartographic developments predate European innovations by several centuries. Whereas European cartographic progress -- and in particular the search for a practical solution to the perennial "longitude problem" at sea --…
We prove that under mild hypothesis rational maps on a surface preserving webs are of Latt\`es type. We classify endomorphisms of P^2 preserving webs, extending former results of Dabija-Jonsson.
We show that a class of quasiregular Latt\`es maps, called orthotopic Latt\`es maps, are cellular Markov maps. This provides examples of expanding Thurston-type maps that are also uniformly quasiregular, and whose visual metrics are…
After a brief discussion of the history of the problem, we propose a generalization of the map colouring problem to higher dimensions.
This thesis presents methods and datasets to investigate cartographic heritage on a large scale and from a cultural perspective. Heritage institutions worldwide have digitized more than one million maps, and automated techniques now enable…
We extend the notion of 'homomorphism-homogeneity' to a wider class of kinds of maps than previously studied, and we investigate the relations between the resulting notions of homomorphism-homogeneity, giving several examples. We also give…
This is a survey article concerning applications of Hilbert's metric in the analysis and dynamics of linear and nonlinear mappings on cones. It will appear as a chapter in the "Handbook of Hilbert geometry", ed. G. Besson, A. Papadopoulos…
A conjecture regarding the structure of expander graphs is discussed.
In the article a technique of the usage of $f$-continuous functions (on mappings) and their families is developed. A proof of the Urysohn's Lemma for mappings is presented and a variant of the Brouwer-Tietze-Urysohn Extension Theorem for…
We study cubic rational maps that take lines to plane curves. A complete description of such cubic rational maps concludes the classification of all planarizations, i.e., maps taking lines to plane curves.
This is an expository paper on the subject of the title. It assumes basic scheme theory, commutative and homological algebra.
The goal of this note is to provide a constructive version of the proof of local structure of etale algebras.
These notes present an approach to obtaining monoid operations which are compatible with a given family of mappings in the sense that the mappings become left translations in the monoid. This can be applied to various situations such as the…
The Lang map, namely the universal dominant rational map to a variety of general type, is constructed and briefly discussed in relation with arithmetic conjectures of Harris, Lang and Manin. Existence of the Lang map follows from the…
This is the direct continuation of the paper "Mapping properties of Fourier transforms" (arXiv:2112.04896) using the same notation as there without further explanations. It deals with continuous and compact mappings of the Fourier transform…
In this paper we discuss about properties of lattices and its application in theoretical and algorithmic number theory. This result of Minkowski regarding the lattices initiated the subject of Geometry of Numbers, which uses geometry to…
The de Sitter manifold admits a wide variety of interesting coordinatizations. The 'atlas' is a compilation of the coordinate charts referenced throughout the literature, and is presented in the form of tables, the starting point being the…
Cartograms combine statistical and geographical information in thematic maps, where areas of geographical regions (e.g., countries, states) are scaled in proportion to some statistic (e.g., population, income). Cartograms make it possible…
This is an expository paper about the topics listed in the title.