Ketty Abaroa de Rezende

Realizability of the Morse polytope

In this article we will show that, in general, for each integral point (γ0,...,γn) in the Morse polytope,Pκ(ho, ...,hn), one can associate an abstract Lyapunov graphL(ho, ...,hn,κ) withntd-labelling and realize a corresponding flow onMn, where the Betti numbers ofMn satisfy βj(Mn)=βn−j(Mn)=γj for all 0

Dynamical and Topological Aspects of Lyapunov Graphs

In this survey we present the interplay between topological dynamical systems theory with network flow theory in order to obtain a continuation result for abstract Lyapunov graphsL(h0, …, hn, k) in dimensionn with cycle numberk. We also show that an abstract Lyapunov graph satisfies the Poincaré-Hopf inequalities if and only if it satisfies the Morse inequalities and the first Betti number γ1 is greater than or equal tok. We define the Morse polytope determined by the Morse inequalities and describe some of its geometrical properties.

Connection matrices for Morse-Bott flows

A Connection Matrix Theory approach is presented for Morse-Bott flows

DISCRETE CONLEY INDEX THEORY FOR ZERO DIMENSIONAL BASIC SETS

\varphi

Smale flows on S-2 x S-1

on smooth closed

Isolating blocks for Morse flows

n

Isolating Blocks for Periodic Orbits

-manifolds by characterizing the set of connection matrices in terms of Morse-Smale perturbations. Further results are obtained on the effect on the set of connection matrices

An Algorithmic Approach to Algebraic and Dynamical Cancellations associated to a Spectral Sequence

\mathcal{CM}(S)

Lyapunov graphs for circle valued functions

caused by changes in the partial orderings and in the Morse decompositions of an isolated invariant set

Cancellations for circle-valued Morse functions via spectral sequences

S