Our main result states that every fixed-point free continuous self-map of ℝⁿ is colorable. This result can be reformulated as follows: A continuous map f: ℝⁿ → ℝⁿ is fixed-point free iff f̃: βℝⁿ → βℝⁿ is fixed-point free. We also obtain a generalization of this fact and present some examples
We give an explicit expression of a two-parameter family of Flensted-Jensen’s functions on a concrete realization of the universal covering group of . We prove that these functions are, up to a phase factor, radial eigenfunctions of the Landau Hamiltonian on the hyperbolic disc with a magnetic field strength proportional to , and corresponding to the eigenvalue .
We study the prolongation of semibasic projectable tangent valued -forms on fibered manifolds with respect to a bundle functor on local isomorphisms that is based on the flow prolongation of vector fields and uses an auxiliary linear -th order connection on the base manifold, where is the base order of . We find a general condition under which the Frölicher-Nijenhuis bracket is preserved. Special attention is paid to the curvature of connections. The first order jet functor and the tangent...
It is proved that near a compact, invariant, proper subset of a C⁰ flow on a locally compact, connected metric space, at least one, out of twenty eight relevant dynamical phenomena, will necessarily occur. Theorem 1 shows that the connectedness of the phase space implies the existence of a considerably deeper classification of topological flow behaviour in the vicinity of compact invariant sets than that described in the classical theorems of Ura-Kimura and Bhatia. The proposed classification brings...
[For the entire collection see Zbl 0699.00032.] The author defines a general notion of a foliated groupoid over a foliation with singularities, within the framework of a (known) general notion of a differentiable structure. Then, he generalizes the classical correspondence between the subalgebras of Lie algebras and the subgroups of the corresponding Lie groups for this type of pseudogroups.