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Periodic problems for ODEs via multivalued Poincaré operators

Lech Górniewicz (1998)

Archivum Mathematicum

We shall consider periodic problems for ordinary differential equations of the form x ' ( t ) = f ( t , x ( t ) ) , x ( 0 ) = x ( a ) , where f : [ 0 , a ] × R n → R n satisfies suitable assumptions. To study the above problem we shall follow an approach based on the topological degree theory. Roughly speaking, if on some ball of R n , the topological degree of, associated to (), multivalued Poincaré operator P turns out to be different from zero, then problem () has solutions. Next by using the multivalued version of the classical Liapunov-Krasnoselskǐ guiding potential...

Periodic segments and Nielsen numbers

Klaudiusz Wójcik (1999)

Banach Center Publications

We prove that the Poincaré map φ ( 0 , T ) has at least N ( h ˜ , c l ( W 0 W 0 - ) ) fixed points (whose trajectories are contained inside the segment W) where the homeomorphism h ˜ is given by the segment W.

Phantom maps and purity in modular representation theory, I

D. Benson, G. Gnacadja (1999)

Fundamenta Mathematicae

Let k be a field and G a finite group. By analogy with the theory of phantom maps in topology, a map f : M → ℕ between kG-modules is said to be phantom if its restriction to every finitely generated submodule of M factors through a projective module. We investigate the relationships between the theory of phantom maps, the algebraic theory of purity, and Rickard's idempotent modules. In general, adding one to the pure global dimension of kG gives an upper bound for the number of phantoms we need...

P-localization of some classes of groups.

Augusto Reynol Filho (1993)

Publicacions Matemàtiques

The aim for the present paper is to study the theory of P-localization of a group in a category C such that it contains the category of the nilpotent groups as a full sub-category. In the second section we present a number of results on P-localization of a group G, which is the semi-direct product of an abelian group A with a group X, in the category G of all groups. It turns out that the P-localized (GP) is completely described by the P-localized XP of X, A and the action w of X on A. In the third...

Poincaré duality and commutative differential graded algebras

Pascal Lambrechts, Don Stanley (2008)

Annales scientifiques de l'École Normale Supérieure

We prove that every commutative differential graded algebra whose cohomology is a simply-connected Poincaré duality algebra is quasi-isomorphic to one whose underlying algebra is simply-connected and satisfies Poincaré duality in the same dimension. This has applications in rational homotopy, giving Poincaré duality at the cochain level, which is of interest in particular in the study of configuration spaces and in string topology.

Poincaré - Verdier duality in o-minimal structures

Mário J. Edmundo, Luca Prelli (2010)

Annales de l’institut Fourier

Here we prove a Poincaré - Verdier duality theorem for the o-minimal sheaf cohomology with definably compact supports of definably normal, definably locally compact spaces in an arbitrary o-minimal structure.

Currently displaying 21 – 40 of 86