363 research outputs found
Analytical Study of the Julia Set of a Coupled Generalized Logistic Map
A coupled system of two generalized logistic maps is studied. In particular
influence of the coupling to the behaviour of the Julia set in two dimensional
complex space is analyzed both analytically and numerically. It is proved
analytically that the Julia set disappears from the complex plane uniformly as
a parameter interpolates from the chaotic phase to the integrable phase, if the
coupling strength satisfies a certain condition.Comment: 30pages, 22figure
Euclidean and hyperbolic lenghs of images of arcs
Let be a function that is analytic in the unit disc. We give new
estimates, and new proofs of existing estimates, of the Euclidean length of the
image under of a radial segment in the unit disc. Our methods are based on
the hyperbolic geometry of plane domains, and we address some new questions
that follow naturally from this approach.Comment: 26 page
On S-duality for Non-Simply-Laced Gauge Groups
We point out that for N=4 gauge theories with exceptional gauge groups G_2
and F_4 the S-duality transformation acts on the moduli space by a nontrivial
involution. We note that the duality groups of these theories are the Hecke
groups with elliptic elements of order six and four, respectively. These groups
extend certain subgroups of SL(2,Z) by elements with a non-trivial action on
the moduli space. We show that under an embedding of these gauge theories into
string theory, the Hecke duality groups are represented by T-duality
transformations.Comment: 8 pages, latex. v2: references adde
Electrical networks on -simplex fractals
The decimation map for a network of admittances on an
-simplex lattice fractal is studied. The asymptotic behaviour of
for large-size fractals is examined. It is found that in the
vicinity of the isotropic point the eigenspaces of the linearized map are
always three for ; they are given a characterization in terms of
graph theory. A new anisotropy exponent, related to the third eigenspace, is
found, with a value crossing over from to
.Comment: 14 pages, 8 figure
Non-Coexistence of Infinite Clusters in Two-Dimensional Dependent Site Percolation
This paper presents three results on dependent site percolation on the square
lattice. First, there exists no positively associated probability measure on
{0,1}^{Z^2} with the following properties: a) a single infinite 0cluster exists
almost surely, b) at most one infinite 1*cluster exists almost surely, c) some
probabilities regarding 1*clusters are bounded away from zero. Second, we show
that coexistence of an infinite 1*cluster and an infinite 0cluster is almost
surely impossible when the underlying probability measure is ergodic with
respect to translations, positively associated, and satisfies the finite energy
condition. The third result analyses the typical structure of infinite clusters
of both types in the absence of positive association. Namely, under a slightly
sharpened finite energy condition, the existence of infinitely many disjoint
infinite self-avoiding 1*paths follows from the existence of an infinite
1*cluster. The same holds with respect to 0paths and 0clusters.Comment: 17 pages, 1 figur
On the Plants Leaves Boundary, "Jupe \`a Godets" and Conformal Embeddings
The stable profile of the boundary of a plant's leaf fluctuating in the
direction transversal to the leaf's surface is described in the framework of a
model called a "surface \`a godets". It is shown that the information on the
profile is encoded in the Jacobian of a conformal mapping (the coefficient of
deformation) corresponding to an isometric embedding of a uniform Cayley tree
into the 3D Euclidean space. The geometric characteristics of the leaf's
boundary (like the perimeter and the height) are calculated. In addition a
symbolic language allowing to investigate statistical properties of a "surface
\`a godets" with annealed random defects of curvature of density is
developed. It is found that at the surface exhibits a phase transition
with critical exponent from the exponentially growing to the flat
structure.Comment: 17 pages (revtex), 8 eps-figures, to appear in Journal of Physics
Invariant varieties of periodic points for some higher dimensional integrable maps
By studying various rational integrable maps on with
invariants, we show that periodic points form an invariant variety of dimension
for each period, in contrast to the case of nonintegrable maps in which
they are isolated. We prove the theorem: {\it `If there is an invariant variety
of periodic points of some period, there is no set of isolated periodic points
of other period in the map.'}Comment: 24 page
Conformal Field Theory and Hyperbolic Geometry
We examine the correspondence between the conformal field theory of boundary
operators and two-dimensional hyperbolic geometry. By consideration of domain
boundaries in two-dimensional critical systems, and the invariance of the
hyperbolic length, we motivate a reformulation of the basic equation of
conformal covariance. The scale factors gain a new, physical interpretation. We
exhibit a fully factored form for the three-point function. A doubly-infinite
discrete series of central charges with limit c=-2 is discovered. A
correspondence between the anomalous dimension and the angle of certain
hyperbolic figures emerges. Note: email after 12/19: [email protected]: 7 pages (PlainTeX
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