We prove a generalization of the Poincaré-Birkhoff theorem for the open annulus showing that if a homeomorphism satisfies a certain twist condition and the nonwandering set is connected, then there is a fixed point. Our main focus is the study of bounded homeomorphisms of the open annulus. We prove a fixed point theorem for bounded homeomorphisms and study the special case of those homeomorphis...

We describe a circle of ideas relating the dynamics of 2-dimensional homeomorphisms to that of 1-dimensional endomorphisms. This is used to introduce a new class of maps generalizing that of Thurston’s pseudo-Anosov homeomorphisms.

In this paper we introduce a new class of closed maps namely g#s-closed also homeomorphisms called g#s*-homeomorphisms and prove that the set all form group under operation composition maps.

Several qualitative properties of the conformal homeomorphisms between relative circle domains are proved. In particular, counterexamples are presented to the analog of Koebe's 1=4 Theorem for conformal homeomorphisms between relative circle domains in simply connected domains, and for isomorphisms of disk packings.

Let f be an uncountable, M -multiply orthogonal domain. Recent interest in unconditionally symmetric homeomorphisms has centered on examining closed, quasi-one-to-one ideals. We show that e is not diffeomorphic to H̄. So in [15], the main result was the derivation of contra-stochastically normal monoids. Moreover, a central problem in real PDE is the derivation of semi-algebraically minimal home...

The Hausdorff distance, the Gromov-Hausdorff, the Fréchet and the natural pseudo-distances are instances of dissimilarity measures widely used in shape comparison. We show that they share the property of being defined as infρ F (ρ) where F is a suitable functional and ρ varies in a set of correspondences containing the set of homeomorphisms. Our main result states that the set of homeomorphisms...

"We study the distortion features of homeomorphisms Sobolev class $W^{1,1}_{\rm loc}$ admitting integrability for $p$-outer dilatation. We show that such mappings belong to $W^{1,n-1}_{\rm loc},$ are differentiable almost everywhere and possess absolute continuity in measure. In addition, both ring lower $Q$-homeomorphisms with appropriate measurable functions $Q.$ This allows us derive various...

Lehmer’s question is equivalent to one about generalized growth rates of Lefschetz numbers of iterated pseudo-Anosov surface homeomorphisms. One need consider only homeomorphisms that arise as monodromies of fibered knots in lens spaces L(n, 1), n > 0. Lehmer’s question for Perron polynomials is equivalent to one about generalized growth rates of words under injective free group endomorphisms.

We describe homotopy classes of self-homeomorphisms of solenoids and Knaster continua. In particular, we demonstrate that homeomorphisms within one homotopy class have the same (explicitly given) topological en-tropy and that they are actually semi-conjugeted to an algebraic homeomor-phism in the case when the entropy is positive.