Jaroslaw Kwapisz

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For a class of Hamiltonian systems in R 4 the set of homoclinic and hete-roclinic orbits which connect saddle-focus equilibria is studied using a vari-ational approach. The oscillatory properties of a saddle-focus equilibrium and the variational nature of the problem give rise to connections in many homotopy classes of the connguration plane punctured at(More)
The extended Fisher Kolmogorov equation, u t = ?u xxxx + u xx +u?u 3 , > 0, models a binary system near the Lifshitz critical point and is known to exhibit a stationary heteroclinic solution joining the equilibria 1. For the classical case, = 0, the heteroclinic is u(x) = tanh(x= p 2) and is unique up to the obvious symmetries. We prove the conjecture that(More)
In generalizing the classical theory of circle maps, we study the rotation set for maps of the real line x 7 ! f(x) with almost periodic displacement f(x) ? x. Such maps are in one-to-one correspondence with maps of compact abelian topological groups that have a dense 1-parameter subgroup preserved by the dynamics. For homeomorphisms, we show existence of(More)
Motivated by the computations in the theory of cohomological Conley index, cocyclic subshifts are the supports of locally constant matrix cocycles on the full shift over a nite alphabet. They properly generalize sooc systems and topological Markov chains; and, via the Wedderburn-Artin theory of nite-dimensional algebras, admit a similar structure theory(More)
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