Recall the notion due to W. Browder of a Poincaré embedding [Br1, Br3, Br2, Br4, Wa, Ra, Wi1, Wi2], which is the homotopy analogue of a smooth embedding of manifolds. Let (M,A) be a simply connected m-dimensional (finite) Poincaré pair. A Poincaré embedding of (M,A) in the sphere S will mean a finite CW-complex W and a map f : A −→ W , such that the homotopy pushout M ∪ι A× [0, 1] ∪f W is homot...

Poincaré maps often prove to be invaluable tools in the study of long-term behaviour and qualitative properties of a given dynamical system. While the analytic theory of these maps is fully explored, finding numerical algorithms that allow the computation of Poincaré maps in concrete problems is far from trivial. For the verification it is desirable to approximate the Poincaré map over as large...

This article presents a new definition of Branson’s Q-curvature in even dimensional conformal geometry. The Q-curvature is a generalization of the scalar curvature in dimension 2: it satisfies an analogous transformation law under conformal rescalings of the metric and on conformally flat manifolds its integral is a multiple of the Euler characteristic. Our approach is motivated by the recent w...

In 1883–1884, Henri Poincaré announced the result about the structure of the set of zeros of function f : I → R, or alternatively the existence of solutions of the equation f x 0. In the case n 1 the Poincaré Theorem is well known Bolzano Theorem. In 1940Miranda rediscovered the Poincaré Theorem. Except for few isolated results it is essentially a non-algorithmic theory. The aim of this article...

The space-time symmetry of noncommutative quantum field theories with a deformed quantization is described by the twisted Poincaré algebra, while that of standard commutative quantum field theories is described by the Poincaré algebra. Based on the equivalence of the deformed theory with a commutative field theory, the correspondence between the twisted Poincaré symmetry of the deformed theory ...

Based on the d’Alembert-Lagrange-Poincaré variational principle, we formulate general equations of motion for mechanical systems subject to nonlinear nonholonomic constraints, that do not involve Lagrangian undetermined multipliers. We write these equations in a canonical form called the Poincaré-Hamilton equations, and study a version of corresponding Poincaré-Cartan integral invariant which a...