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- D . Kalies, Jaroslaw Kwapisz, Robert C. Vandervorst
- 1997

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)

- Jaroslaw Kwapisz
- 1997

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)

- Jaroslaw Kwapisz
- 2001

We describe homotopy classes of self-homeomorphisms of solenoids and Knaster continua. In particular, we demonstrate that homeomorphisms within one homotopy class have the same (explicitly given) topological en-tropy and that they are actually semi-conjugeted to an algebraic homeomor-phism in the case when the entropy is positive.

- Jaroslaw Kwapisz
- 1992

We construct a diffeomorphism of the two-dimensional torus which is isotopic to the identity and whose rotation set is not a polygon.

- Jaroslaw Kwapisz
- 1999

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)

- Jaroslaw Kwapisz
- Journal of Graph Theory
- 1996

We provide upper estimates on the spectral radius of a directed graph. In particular we prove that the spectral radius is bounded by the maximum of the geometric mean of in-degree and out-degree taken over all vertices.

- Jaroslaw Kwapisz
- 1997

We give a geometric proof of stability for spatially nonho-mogeneous equilibria in the singular perturbation problem u t = 2 u xx + f(x; u); t 2 R + ; ?1 u 1, with the Neumann boundary conditions on x 2 0; 1]. The nonlinearity is of the form f(x; u) := (1 ?u 2)(u ?c(x)) where c(x) is merely continuous with a nite number of zeros. The strength of the method… (More)

- Jaroslaw Kwapisz
- 1999

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)

- D . Kalies, Jaroslaw Kwapisz, Robert C. Vandervorst
- 1998

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)

- Jaroslaw Kwapisz
- 1994

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