Pełnotekstowe zasoby PLDML oraz innych baz dziedzinowych są już dostępne w nowej Bibliotece Nauki.
Zapraszamy na https://bibliotekanauki.pl
Preferencje help
Polish version English version Język
Widoczny [Schowaj] Abstrakt
Liczba wyników

Znaleziono wyników: 7

Liczba wyników na stronie
first rewind previous Strona / 1 next fast forward last

Wyniki wyszukiwania

Wyszukiwano:
w słowach kluczowych:  Conley index
help Sortuj według:

help Ogranicz wyniki do:
first rewind previous Strona / 1 next fast forward last
1
Content available remote

Connection matrix theory for discrete dynamical systems

100%
Bartłomiejczyk P., Dzedzej Z.
Banach Center Publications
|
1999
|
tom 47
|
nr 1
67-78
EN
In [C] and [F1] the connection matrix theory for Morse decomposition is developed in the case of continuous dynamical systems. Our purpose is to study the case of discrete time dynamical systems. The connection matrices are matrices between the homology indices of the sets in the Morse decomposition. They provide information about the structure of the Morse decomposition; in particular, they give an algebraic condition for the existence of connecting orbit set between different Morse sets.
2
Content available remote

Reconstructing the global dynamics of attractors via the Conley index

100%
McCord C.
Banach Center Publications
|
1999
|
tom 47
|
nr 1
145-156
EN
Given an unknown attractor 𝓐 in a continuous dynamical system, how can we discover the topology and dynamics of 𝓐? As a practical matter, how can we do so from only a finite amount of information? One way of doing so is to produce a semi-conjugacy from 𝓐 onto a model system 𝓜 whose topology and dynamics are known. The complexity of 𝓜 then provides a lower bound for the complexity of 𝓐. The Conley index can be used to construct a simplicial model and a surjective semi-conjugacy for a large class of attractors. The essential features of this construction are that the model 𝓜 can be explicitly described; and that the finite amount of information needed to construct it is computable.
3
Content available remote

Index filtrations and Morse decompositions for discrete dynamical systems

100%
Bartłomiejczyk P., Dzedzej Z.
Annales Polonici Mathematici
|
1999
|
tom 72
|
nr 1
51-70
EN
On a Morse decomposition of an isolated invariant set of a homeomorphism (discrete dynamical system) there are partial orderings defined by the homeomorphism. These are called admissible orderings of the Morse decomposition. We prove the existence of index filtrations for admissible total orderings of a Morse decomposition and introduce the connection matrix in this case.
4
Content available remote

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

100%
Srzednicki R.
Annales Mathematicae Silesianae
|
2015
|
tom 29
|
nr 1
7-17
EN
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.
5
Content available remote

An attraction result and an index theorem for continuous flows on $ℝ^n × [0,∞)$

100%
Wójcik K.
Annales Polonici Mathematici
|
1996-1997
|
tom 65
|
nr 3
203-211
EN
We study the behavior of a continuous flow near a boundary. We prove that if φ is a flow on $E = ℝ^{n+1}$ for which $∂E = ℝ^n × {0}$ is an invariant set and S ⊂ ∂E is an isolated invariant set, with non-zero homological Conley index, then there exists an x in E\∂E such that either α(x) or ω(x) is in S. We also prove an index theorem for a flow on $ℝ^n × [0,∞)$.
6
Content available remote

Connection matrix pairs

88%
Richeson D.
Banach Center Publications
|
1999
|
tom 47
|
nr 1
219-232
EN
We discuss the ideas of Morse decompositions and index filtrations for isolated invariant sets for both single-valued and multi-valued maps. We introduce the definition of connection matrix pairs and present the theorem of their existence. Connection matrix pair theory for multi-valued maps is used to show that connection matrix pairs obey the continuation property. We conclude by addressing applications to numerical analysis. This paper is primarily an overview of the papers [R1] and [R2].
7
Content available remote

Equivariant Morse equation

75%
Styborski M.
Open Mathematics
|
2012
|
tom 10
|
nr 6
2138-2159
EN
The paper is concerned with the Morse equation for flows in a representation of a compact Lie group. As a consequence of this equation we give a relationship between the equivariant Conley index of an isolated invariant set of the flow given by .x = −∇f(x) and the gradient equivariant degree of ∇f. Some multiplicity results are also presented.
first rewind previous Strona / 1 next fast forward last
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.