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Let M be either a topological manifold, a Hilbert cube manifold, or a Menger manifold and let D be an arbitrary countable dense subset of M. Consider the topological group À(M,D) which consists of all autohomeomor-phisms of M that map D onto itself equipped with the compact-open topol-ogy. We present a complete solution to the topological classification… (More)
Dedicated to our friend Imre Bárány on the occasion of his 50-th birthday. Abstract For any λ > 1 we construct a periodic and locally finite packing of the plane with ellipses whose λ-enlargement covers the whole plane. This answers a question of Imre Bárány. On the other hand, we show that if C is a packing in the plane with circular discs of radius at… (More)
In this paper we describe the intimate interplay between certain classes of dynamical systems and a holomorphic curve theory. There are many aspects touching areas like Gromov-Witten invariants, quantum cohomology, symplectic homology, Seiberg-Witten invariants, Hamilto-nian dynamics and more. Emphasized is this interplay in real dimension three. In this… (More)
Using the theory of plugs and the self-insertion construction due to the second author, we prove that a foliation of any codimension of any manifold can be modified in a real analytic or piecewise-linear fashion so that all minimal sets have codimension 1. In particular, the 3-sphere S 3 has a real analytic dynamical system such that all limit sets are… (More)
We construct a proper C 2-smooth function on R 4 such that its Hamiltonian flow has no periodic orbits on at least one regular level set. This result can be viewed as a C 2-smooth counterexample to the Hamiltonian Seifert conjecture in dimension four.
The collection of works for this special issue was inspired by the presentations given at the 2011 AMS Special Session on Formal Mathematics for Mathematicians: Developing Large Repositories of Advanced Mathematics. The issue features a collection of articles by practitioners of formalizing proofs who share a deep interest in making computerized mathematics… (More)
W e construct counterexamples to some conjectures of J. Birman and R. F. Williams concerning the knotting and linking of closed orbits of ows on 3-manifolds. By establishing the existence of universal templates," we produce examples of ows on S 3 containing closed orbits of all knot and link types simultaneously. In particular, the set of closed orbits of… (More)
It is shown that for every triple of integers (α, β, γ) such that α ≥ 1, β ≥ 1, and γ ≥ 2, there is a homogeneous, non-bihomogeneous continuum whose every point has a neighborhood homeomorphic the Cartesian product of Menger compacta µ α × µ β × µ γ. In particular, there is a homogeneous, non-bihomogeneous, Peano continuum of covering dimension four.
If C is a Jordan curve on the plane and P, Q ∈ C, then the segment P Q is called a chord of the curve C. A point inside the curve is called equichordal if every two chords through this point have the same length. Fujiwara in 1916 and independently Blaschke, Rothe and Weitzenböck in 1917 asked whether there exists a curve with two distinct equichordal points… (More)
The pseudo-circle is known to be nonhomogeneous. The original proofs of this fact were discovered independently by L. Fearnley  and J.T. Rogers, Jr. . The purpose of this paper is to provide an alternative, very short proof based on a result of D. Bellamy and W. Lewis .