10 ENGLISH BOOKS RELATING TO «LOXODROMIC»
Discover the use of
loxodromic in the following bibliographical selection. Books relating to
loxodromic and brief extracts from same to provide context of its use in English literature.
1
Hyperbolic Manifolds and Discrete Groups
loxodromic: Z(g) > 0; ' parabolic: £(g) = 0 but g does not have a fixed point in IHI"; '
elliptic: g fixes a point in ll-ll”. Any loxodromic element h has a unique invariant
geodesic Ah in ll-ll". This invariant geodesic is called the axis of h. The restriction
...
2
Invitation to the Mathematics of Fermat-Wiles
Itis clearthatthe loxodromic functions of multiplicatorq form a field,whichwe call Lq
. It is also clear that the loxodromic functions satisfy structure theorems analogous
to the theorems concerning elliptic functions. Theorem 2.9.1 Every entire ...
3
Hyperbolic Geometry from a Local Viewpoint
Lemma 5.1.1 If G is a non-elementary group then G must contain infinitely many
distinct loxodromic elements. Proof. First assume there are no parabolic or
loxodromic elements. Because the group is non-elementary, there must be at
least two ...
Linda Keen, Nikola Lakic, 2007
4
Conformal Geometry of Discrete Groups and Manifolds
Namely, we say that loxodromic fixed points (i.e., fixed points of loxodromic
elements) are dense in A(G) x A(G) if, for any disjoint open neighborhoods V\ and
V2 of arbitrary limit points ATI and *2, there exists a loxodromic element g e G
with ...
Boris Nikolaevich Apanasov, 2000
5
Discontinuous Groups and Riemann Surfaces: Proceedings
Proceedings Leon Greenberg. Then g(x) = gfg-1(g(x)) = f(g(x)). Thus g leaves fp,
°°| invariant. Since g(:*>) = ~, g(p) = p. We now consider the general case, where
F" need not be trivial. Let g ( F" and let f be a loxodromic element in F, with fixed ...
6
Recreations in mathematics and natural philosophy, ...
But, for the sake of farther illustration, let us suppose a loxodromic line inclined to
the meridian at an angle of 60 degrees, with its infinite circumvolutions around
the pole ; if we employ the following proportion, As the cosine of 60 degrees, ...
Jacques Ozanam, Jean Étienne Montucla, 1803
7
Discrete Groups in Space and Uniformization Problems
g is a loxodromic element of a non-elementary Klelnian group GcMob(n), then for
each open neighbourhood U of any limit point xeA(G) there exists a g, e G such
that the fixed points of the loxodromic element g\gg? lie in U. We say that the ...
8
The Coxeter Legacy: Reflections and Projections
Next, consider a simple closed geodesic g of length / bounded from above by en.
g gives rise to a loxodromic element 7 6 F with translational length l(g) along its
axis a. An n-dimensional collar theorem due to C. Cao and P. Waterman [4] ...
Harold Scott Macdonald Coxeter, Chandler Davis, Erich W. Ellers
9
Complex Kleinian Groups
(iv) A loxodromic element belongs to one and only one of the following four
classes: loxo-parabolic, homothety, screw or strongly loxodromic. Proof. Let ˆg be
an element in PSL(3,C) \ {Id}, and g ∈ SL(3,C) a lift with eigenvalues λi, i = 1,2,3.
Angel Cano, Juan Pablo Navarrete, Seade Kuri José Antonio, 2012
10
Discontinuous Groups and Automorphic Functions
This is no longer possible where there is more than one limit point.5 THEOREM.
If Y has more than one point, I' contains hyperbolic or loxodromic substitutions.
Assume I' contains only elliptic and parabolic elements. I' does not consist only of
...
NEWS ITEMS WHICH INCLUDE THE TERM «LOXODROMIC»
Find out what the national and international press are talking about and how the term
loxodromic is used in the context of the following news items.
There's no perfect map but Mercator's is marvellous
Navigators could now plot a loxodromic course as a straight line, joining their departure point and destination, and follow this course across the ... «Irish Times, May 15»
