Wyniki wyszukiwania

Sortuj według:

Ogranicz wyniki do:

On Computer-Assisted Proving The Existence Of Periodic And Bounded Orbits

100%

Srzednicki R.

Annales Mathematicae Silesianae

2015

tom 29

nr 1

7-17

We announce a new result on determining the Conley index of the Poincaré map for a time-periodic non-autonomous ordinary differential equation. The index is computed using some singular cycles related to an index pair of a small-step discretization of the equation. We indicate how the result can be applied to computer-assisted proofs of the existence of bounded and periodic solutions. We provide also some comments on computer-assisted proving in dynamics.

A cohomological index of Fuller type for parameterized set-valued maps in normed spaces

68%

Skiba R.

Open Mathematics

2014

tom 12

nr 8

1164-1197

We construct a cohomological index of the Fuller type for set-valued flows in normed linear spaces satisfying the properties of existence, excision, additivity, homotopy and topological invariance. In particular, the constructed index detects periodic orbits and stationary points of set-valued dynamical systems, i.e., those generated by differential inclusions. The basic methods to calculate the index are also presented.

Ograniczanie wyników

1 Annales Mathematicae Silesianae

1 Open Mathematics

1 Skiba R.

1 Srzednicki R.

1 2015

1 2014

Wyniki wyszukiwania

On Computer-Assisted Proving The Existence Of Periodic And Bounded Orbits

A cohomological index of Fuller type for parameterized set-valued maps in normed spaces