M. Razvan

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math.DS2001

On the Poincare Index of Isolated Invariant Sets

M. R. Razvan, M. Fotouhi Firoozabad

In this paper, we use Conley index theory to examine the Poincare index of an isolated invariant set. We obtain some limiting conditions on a critical point of a planar vector fiel…

math.DS2000

Lusternik-Schnirelmann Theory for a Morse Decomposition

M. R. Razvan

Let $ϕ^{t}$ be a continuous flow on a metric space $X$ and $I$ be an isolated invariant set with an index pair $(N, L)$ and a Morse decomposition ${M_{i}}_{i = 1}^{n}$ . For every category…

math.DS2000

On Conley's Fundamental Theorem of Dynamical Systems

M. R. Razvan

In this paper, we generalize Conley's fundamental theorem of dynamical systems in Conley index theory. We also conclude the existence of regular index filtration for every Morse de…

math.DS2000

Palais-Smale Condition, Index Pairs and Critical Point Theory

M. R. Razvan

This paper is concerned with index pairs in the sense of Conley index theory for flows relative to pseudo-gradient vector fields for $C^{1}$ -functions satisfying Palais-Smale conditi…