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Showing 1 to 17 of 17 for “"Cantor set"”.
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Strange Attractors of Uniform Flows (Cantor Set, Solenoid)
… to these tori are derived for an arbitrary set to be an orbitally stable attractor. When the cross-section of an orbitally stable attractor is a Cantor set, then first return map is found to be conjugate to an irrational rotation on a certain compact abelian group. New examples are …
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The noncommutative geometry of ultrametric cantor sets
… of a manifold is created for an ultrametric Cantor set using the techniques of Noncommutative Geometry. In particular, a spectral triple is created that can recover much of the fractal geometry of the original Cantor set. It is shown that this spectral triple can recover the metric, the upper …
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Continued Radicals and Cantor Sets
<p>We examine the formation of sets homeomorphic to the ternary Cantor set by continued radicals. We determine properties of bridges and gaps and calculate the thickness of the Cantor set. From this we apply information from continued fractions to continued radicals to obtain new results. We also …
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Dynamics of Cubic Rational Maps Under Certain Constraints on Critical Points
<p>There is a neat dichotomy for the Julia sets of quadratic rational maps; that is, they are either connected or a Cantor set. In contrast to the quadratic case, the Julia sets of rational maps of of degree ≥ 3 have more variations. In this project, we study the Julia sets of cubic rational maps …
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The diffraction of monsters from complex apertures
… a multi-scale character, such as a pre-fractal Cantor set (that is, a diffraction grating modelled onany finite iteration of the Cantor set). Previous related studies have been concerned predominantly with regimes wherein the outgoing waves are observed in the far field (that is, at large …
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Dynamics of Polish groups
… show that the group of all homeomorphisms of the Cantor set H(2^N) has ample generics, that is, we show that for every m the diagonal conjugacy action g\cdot (h_1, h_2,...,h_m) = (gh_1g^{-1}, gh_2g^{-1},..., gh_mg^{-1}) of H(2^N) on H(2^N)^m has a comeager orbit. This answers a question of Kechris …
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Continued Radicals
… is a continued radical. We consider the set of real numbers S(M) representable as an infinite nested radical whose terms a1, a2, . . . are all from a finite set M. We give conditions on the set M for S(M) to be (a) an interval, and (b) homeomorphic to the Cantor set.
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Integrals of harmonic functions over curves and surfaces
… is estimated for harmonic functions given by the Cantors measures on the unit circle in terms of the porosity of the Cantor set. The exact lower bound of it for all normalized positive harmonic functions in the unit ball of $R\sp{n}$ is established. Also, its value for the functions given by the …
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The Space of Left Orders on a Group
… algebraic group theory, algebraic topology, and set theory. This paper will act as a guide into the world of orderable groups. It begins by enlightening the reader to the fundamental axioms of orderable groups, as well as, noting various important groups on which orders are often considered. We …
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Cantor Minimal Systems and Dimension Groups
… orbit equivalence of minimal Z^d-actions on a Cantor set. The range of such dimension groups for d>1 is still an open question. It appears as if symbolic dynamical systems may be a fruitful approach to this question. In this work, the relationship is explored between Cantor minimal systems, …
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Fractal analysis of topography and reflectance surfaces
… deduced from constructing the Koch curve and the Cantor set. Principles of seven methods (the ruler, box-counting, spectral structure function, intersection methods, cube-counting, and triangular prism methods) for determining the fractal dimensions are illustrated and verified by the Koch curve, …
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Novel ultrasonic transducers and array designs using self-similar fractal geometries
… Sierpinski Gasket, Sierpinski Carpet, Cantor Set and Cantor Tartan. The fractal composite devices were realised as either 1-3 connectivity or 2-2 connectivity configurations and compared with their corresponding equivalent conventional composite counterpart. Finite element modelling was …
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Dynamics of Iterated Functions Systems: Hausdorff Dimension and Related Topics
… explores the Hausdorff dimension of fractal sets generated by iterated function systems (IFS). Hutchinson studied IFS and obtained a useful formula to compute the Hausdorff dimension of fractals generated by a finite family of disjoint similar IFS, where by disjoint we mean the IFS satisfies …
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SOME MAGNETIC PROPERTIES OF BORE CORE SEDIMENTS
… is strongly supported by a fractal model (i.e. a Cantor set) introduced for relating the shortest polarity interval, the transition time and the fractal dimension. Normal and reversed polarity intervals have similar fractal dimensions, suggesting that there is no, statistically, fundamental …
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Discreet dynamical population models : higher dimensional pioneer-climax models
… shift map behavior on an invariant two-component Cantor set for systems containing a climax component. Bifurcation diagrams and Lyapunov diagrams are computed to further illustrate the chaotic dynamics. Finally, the concept of a 3-dimensional horseshoe type map is also used to prove the existence …
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Topological Dynamics On Compact Phase Spaces
… enveloping semigroup, which is a closure of the set of continuous functions on a compact space $X$, was discovered to be an important tool to study dynamical systems. Soon, a realization of the existence of a universal compactification of a phase semigroup with an extended homomorphism onto the …