173,436 research outputs found
Dr. Howard W. Conley
No full textPortrait of Dr. Howard W. Conley. Dr. Conley was the chairman and department director of Orthodontics at the School of Dentistry from 1967 until 1969.10 x 13 c
On the two definitions of the Conley index
No full textThe two definitions of the homotopy equivalences between Conley index spaces of an isolated invariant set, the original one of Conley [C] as completed by the author in [K1] and the more recent definition of Salamon [S], are shown to define the same homotopy classes without reference to the difficult proof of [K1] showing the Conley index to be a connected simple system. The equivalences of the original definition are useful in describing certain geometric situations in terms of the index; examples are given.</p
Conley type index and Hamiltonian inclusions
No full textsummary:This paper is based mainly on the joint paper with W. Kryszewski [Dzedzej, Z., Kryszewski, W.: Conley type index applied to Hamiltonian inclusions. J. Math. Anal. Appl. 347 (2008), 96–112.], where cohomological Conley type index for multivalued flows has been applied to prove the existence of nontrivial periodic solutions for asymptotically linear Hamiltonian inclusions. Some proofs and additional remarks concerning definition of the index and special cases are given
The E-cohomological Conley index, cup-lengths and the Arnold conjecture on T2n
No full textWe show that the E-cohomological Conley index, that was introduced by the first author recently, has a natural module structure. This yields a new cup-length and a lower bound for the number of critical points of functionals on Hilbert spaces. When applied to the setting of the Arnold conjecture, this paves the way to a short proof on tori, where it was first shown by C. Conley and E. Zehnder in 1983
The E-cohomological Conley Index, Cup-Lengths and the Arnold Conjecture on T2n
No full textWe give a new proof of the strong Arnold conjecture for 1-periodic solutions of Hamiltonian systems on tori, that was first shown by C. Conley and E. Zehnder in 1983. Our proof uses other methods and is shorter than the previous one. We first show that the E-cohomological Conley index, that was introduced by the first author recently, has a natural module structure. This yields a new cup-length and a lower bound for the number of critical points of functionals. Then an existence result for the E-cohomological Conley index, which applies to the setting of the Arnold conjecture, paves the way to a new proof of it on tori
On foundations of the Conley index theory
No full textThe Conley index theory was introduced by Charles C. Conley (1933-1984) in [C1] and a major part of the foundations of the theory was developed in Ph. D. theses of his students, see for example [Ch, Ku, Mon]. The Conley index associates the homotopy type of some pointed space to an isolated invariant set of a flow, just as the fixed point index associates an integer number to an isolated set of fixed points of a continuous map. Examples of isolated invariant sets arise naturally in the critical point theory - each isolated critical point of a functional is also an isolated invariant set of its gradient flow. If the critical point is nondegenerate then its Conley index is equal to the homotopy type of the pointed k-sphere, where k is the Morse index of that point. There are other relations to Morse theory, for example a generalization of Morse inequalities can be achieved. The aim of this note is to describe briefly some basic facts of the Conley index theory for (continuous-time) flows. We refer to [C2, Ry, S1, Smo] for a more detailed presentation. We do not touch more advanced topics of the theory: the Conley index as a connected simple system (see [C2, Ku, McM, S1]), connection and transition matrices (see [F1, F2, FM, McM, Mi1, Moe, Re]]), infinite dimensional Conley indices (see [Be, Ry], the Conley index for multivalued flows (see [KM, Mr2]), Conley-type indices for discrete-time flows (see [Mr3, RS, Sz]), equivariant Conley indices (see [Ba, Ge]), and relations to the Floer homology (see [S2]). (The list of bibliography items is far from completeness.) Moreover, we do not present any applications of the index. For some more recent results we refer to [Mi2]. We also refer to the other articles in this Proceedings
Externalities and fundamental nonconvexities : a reconciliation of approaches to general equilibrium externality modeling and implications for decentralization
No full textBy distinguishing between producible and nonproducible public goods, we are able to propose a general equilibrium model with externalities that distinguishes between and encompasses both the Starrett [1972] and Boyd and Conley [1997] type external effects. We show that while nonconvexities remain fundamental whenever the Starrett
type external effects are present, these are not caused by the type discussed in Boyd and Conley. Secondly, we find that the notion of a “public competitive equilibrium”
for public goods found in Foley [1967, 1970] allows a decentralized mechanism, based on both price and quantity signals, for economies with externalities, which is able
to restore the equivalence between equilibrium and efficiency even in the presence of nonconvexities. This is in contrast to equilibrium notions based purely on price signals such as the Pigouvian taxes
Zeta Functions, Periodic Trajectories, and the Conley Index
No full textAbstractWe use the Conley index to produce a simple sufficient condition (stated in terms of the Betti numbers of the cohomology Conley index) for the existence of periodic orbits for flows which admit a cross-section
Master stone cutter Kevin Conley with helper Bill Bisesi
No full textHandwritten in pencil on verso: Master stone cutter Kevin Conley (right) with his (helper) Bill Bisesi. Kevin has worked at the Conley family-owned Banne Monument Co. since the age of nine; S-106-C-EBC-12. Signed: Elinor B. Cahn, 1980
Homotopy invariance of the Conley index and local Morse homology in Hilbert spaces
No full textIn this paper we introduce a new compactness condition — Property-(C) — for flows in (not necessary locally compact) metric spaces. For such flows a Conley type theory can be developed. For example (regular) index pairs always exist for Property-(C) flows and a Conley index can be defined. An important class of flows satisfying the this compactness condition are LS-flows. We apply E-cohomology to index pairs of LS-flows and obtain the E-cohomological Conley index. We formulate a continuation principle for the E-cohomological Conley index and show that all LS-flows can be continued to LS-gradient flows. We show that the Morse homology of LS-gradient flows computes the E-cohomological Conley index. We use Lyapunov functions to define the Morse–Conley–Floer cohomology in this context, and show that it is also isomorphic to the E-cohomological Conley index
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