Mappings of the Sierpinski Curve onto Itself
نویسنده
چکیده
Given two points p and q of the Sierpinski universal plane curve S, necessary and/ or sufficient conditions are discussed in the paper under which there is a mapping I of S onto itself such that I(P) = q and I belongs to one of the following: homeomorphisms, local homeomorphisms, local homeomorphisms in the large sense, open, simple or monotone mappings.
منابع مشابه
3-dimensional Chaotic Dynamics on Jacobian Elliptic Space Curve
Sufficient conditions have been recently given for a classs of ergodic maps of an interval onto itself: I = [0, 1] ⊂ R1 → I and its associated binary function to generate a sequence of independent and idetically distributed (i.i.d.) random variables. Jacobian elliptic Chebyshev map, its derivative and second derivative induce Jacobian elliptic space curve. A mapping of the space curve onto itse...
متن کاملQuasiconformal Harmonic Functions between Convex Domains
We generalize Martio’s paper [14]. Indeed the problem studied in this paper is under which conditions on a homeomorphism f between the unit circle S1 := {z : |z| = 1} and a fix convex Jordan curve γ the harmonic extension of f is a quasiconformal mapping. In addition, we give some results for some classes of harmonic diffeomorphisms. Further, we give some results concerning harmonic quasiconfor...
متن کاملLee-Yang zeros and the Ising model on the Sierpinski Gasket
We study the distribution of the complex temperature zeros for the partition function of the Ising model on a Sierpinski gasket using an exact recursive relation. Although the zeros arrange on a curve pinching the real axis at T = 0 in the thermodynamic limit, their density vanishes asymptotically along the curve approaching the origin. This phenomenon explains the coincidence of the low temper...
متن کاملLocally Sierpinski Julia Sets of Weierstrass Elliptic ℘ Functions
We define a locally Sierpinski Julia set to be a Julia set of an elliptic function which is a Sierpinski curve in each fundamental domain for the lattice. In order to construct examples, we give sufficient conditions on a lattice for which the corresponding Weierstrass elliptic ℘ function is locally connected and quadratic-like, and we use these results to prove the existence of locally Sierpin...
متن کاملLocally Sierpinski Julia Sets of Weierstrass Elliptic P Functions
We define a locally Sierpinski Julia set to be a Julia set of an elliptic function which is a Sierpinski curve in each fundamental domain for the lattice. In order to construct examples, we give sufficient conditions on a lattice for which the corresponding Weierstrass elliptic ℘ function is locally connected and quadratic-like, and we use these results to prove the existence of locally Sierpin...
متن کامل