Related papers: On Latt\`es Maps
In this paper, we introduce some known map projections from a model of the Earth to a flat sheet of paper or map and derive the plotting equations for these projections. The first fundamental form and the Gaussian fundamental quantities are…
In 1986, Oliver Pretzel studied the set of orientations of a connected finite graph $G$ and showed that any two such orientations having the same flow-difference around all closed loops can be obtained from one another by a succession of…
We use the recently introduced \'etale open topology to prove several facts about large fields. We show that these facts lift to a very general topological setting.
Sto\"ilow's theorem from 1928 states that a continuous, open, and light map between surfaces is a discrete map with a discrete branch set. This result implies that such maps between orientable surfaces are locally modeled by power maps…
This paper is devoted to proving an infinite sequence of relations for rooted tree maps. On the way, we also give a basis for the space of rooted tree maps.
This paper investigates some combinatorial and algebraic properties of a Witt type formula for graphs.
The solution of the geodesic problem for an oblate ellipsoid is developed in terms of series. Tables are provided to simplify the computation. [This is an English translation of F. W. Bessel, Astronomische Nachrichten 4(86), 241-254 (1825).…
Presentation of set matrices and demonstration of their efficiency as a tool using the path/cycle problem.
This report is an introduction to mathematical map colouring and the problems posed by Heawood in his paper of 1890. There will be a brief discussion of the Map Colour Theorem; then we will move towards investigating empire maps in the…
Generalized are the investigated in other works of the author transports along paths in fibre bundles to transports along arbitrary maps in them. Their structure and some properties are studied. Special attention is paid to the linear case…
This is a preliminary investigation of the geometry and dynamics of rational maps with only two critical points. (originally titled ``On Bicritical Rational Maps'' in September 1997; revised and retitled April 1999)
The $\lambda$-perfect maps, a generalization of perfect maps (continuous closed maps with compact fibers) are presented. Using $P_\lambda$-spaces and the concept of $\lambda$-compactness some results regarding $\lambda$-perfect maps will be…
We prove that any Latt\`es map can be approximated by strictly postcritically finite rational maps which are not Latt\`es maps.
The evolution of infrastructure networks such as roads and streets are of utmost importance to understand the evolution of urban systems. However, datasets describing these spatial objects are rare and sparse. The database presented here…
This paper uses traditional maps in animations to show traffic congestion effects in London
Let f be a self-map of the set A. We give a necessary and sufficient condition for the existence of a lattice structure on A such that f becomes a lattice endomorphism with respect to this structure.
It is a survey paper on n-dimensional local fields and adeles on n-dimensional schemes.
We use the transport methods developped in [3] to obtain universality results for local statistics of eigenvalues in the bulk and at the edge for $\beta$-matrix models in the multi-cut regime. We construct an approximate transport map…
This note generalizes a result contained in a previous paper [ J. Sanders, Circuit preserving edge maps II, J. Combin. Theory Ser. B 42 (1987), 146-155].
We study the local well-posedness theory for the Schr\"odinger Maps equation. We work in $n+1$ dimensions, for $n \geq 2$, and prove a local well-posedness for small initial data in $H^{\frac{n}{2}+\e}$.