A Combinatorial Construction of Chaotic Homeomorphisms on Manifolds
نویسنده
چکیده
We use a combinatorial idea of Peter Lax to construct, on any compact manifold, a self homeomorphism which is chaotic in the sense of Devaney. Moreover we show that such transformations are dense, with respect to the uniform topology, in the space of volume preserving homeomorphisms of the closed unit cube I n ; n 2: This work extends that of John Oxtoby, who in 1937 proved similar results for transitive transformations.
منابع مشابه
Periodic, Locally Linear, and Chaotic Approximations to Volume Preserving Homeomorphisms
We modify a combinatorial idea of Peter Lax, to uniformly approximate any volume preserving homeomorphism h of the closed unit cube In; n 2; by another one ĥ such that either: (i) ĥ rigidly permutes an in nite family of dyadic cubes of total volume one, or (ii) ĥ is chaotic in the sense of Devaney. The rst result (i) generalizes a similar result of Oxtoby and Ulam, yielding an approximation whi...
متن کاملQuasiconformal Homeomorphisms on Cr 3-manifolds with Symmetries
An extremal quasiconformal homeomorphisms in a class of homeomorphisms between two CR 3-manifolds is an one which has the least conformal distortion among this class. This paper studies extremal quasiconformal homeomorphisms between CR 3-manifolds which admit transversal CR circle actions. Equivariant K-quasiconformal homeomorphisms are characterized by an area-preserving property and the K-qua...
متن کاملRegularity and Extremality of Quasiconformal Homeomorphisms on Cr 3-manifolds
This paper first studies the regularity of conformal homeomorphisms on smooth locally embeddable strongly pseudoconvex CR manifolds. Then moduli of curve families are used to estimate the maximal dilatations of quasiconformal homeomorphisms. On certain CR 3-manifolds, namely, CR circle bundles over flat tori, extremal quasiconformal homeomorphisms in some homotopy classes are constructed. These...
متن کاملConstruction of Combinatorial Manifolds with the Prescribed Sets of Links of Vertices
To each oriented closed combinatorial manifold we assign the set (with repetitions) of isomorphism classes of links of its vertices. The obtained transformation L is the main object of study of the present paper. We pose a problem on the inversion of the transformation L. We shall show that this problem is closely related to N. Steenrod’s problem on realization of cycles and to the Rokhlin-Schw...
متن کاملSmall dilatation pseudo-Anosov homeomorphisms and 3–manifolds
The main result of this paper is a universal finiteness theorem for the set of all small dilatation pseudo-Anosov homeomorphisms φ : S → S, ranging over all surfaces S. More precisely, we consider pseudo-Anosov homeomorphisms φ : S → S with |χ(S)| log(λ(φ)) bounded above by some constant, and we prove that, after puncturing the surfaces at the singular points of the stable foliations, the resul...
متن کامل