Abstract

ZAPATA GOMEZ, Yesenia; DELA-ROSA, Miguel Angel  and  REMIGIO-JUAREZ, Jair. Conley Index and continuous dynamical systems. Rev. Mat [online]. 2021, vol.28, n.2, pp.237-259. ISSN 1409-2433.  http://dx.doi.org/10.15517/rmta.v28i2.44748.

The goal of this work is to apply topological methods to obtain results about continuous flows determined by differential equations. Specifically, we apply the Conley Index Theory to prove that, under certain assumptions, there is an invariant set which contains a non-trivial solution. The construction of this invariant set is purely topological and depends on the flow of the differential equation, but the existence of the non-trivial solution is obtained as an application of homological techniques. In this survey paper we develop and precise these ideas, and in order to get a better understanding we include some examples and computations in some ordinary differential equations. This work is mostly based on [6].

Keywords : Conley index; homology; continuous dynamics; homotopic equivalence; Wazewski principle..

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