منابع مشابه
Lusternik – Schnirelman Theory and Dynamics
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S. P. Novikov developed an analog of the Morse theory for closed 1-forms. In this paper we suggest an analog of the Lusternik Schnirelman theory for closed 1-forms. For any cohomology class ξ ∈ H(X,R) we define an integer cl(ξ) (the cuplength associated with ξ); we prove that any closed 1-form representing ξ has at least cl(ξ)− 1 critical points. The number cl(ξ) is defined using cup-products i...
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In a preceding note [3], we observed that under assumptions of polynomial growth on F, G, FPa, and GPa in u and its derivatives, ellipticity and positivity for B, and positivity for A, there exists an eigenf unction of the pair (A, B), i.e. a solution u of the equation Bu=\Au with X in R, with f(u) prescribed and u satisfying a null variational boundary condition corresponding to a given closed...
متن کاملun 2 00 1 Zeros of closed 1 - forms , homoclinic orbits , and Lusternik - Schnirelman theory
In this paper we study topological lower bounds on the number of zeros of closed 1-forms without Morse type assumptions. We prove that one may always find a representing closed 1-form having at most one zero. We introduce and study a generalization cat(X, ξ) of the notion of Lusternik Schnirelman category, depending on a topological space X and a 1-dimensional real cohomology class ξ ∈ H1(X;R)....
متن کاملZeros of closed 1-forms, homoclinic orbits, and Lusternik - Schnirelman theory
In this paper we study topological lower bounds on the number of zeros of closed 1-forms without Morse type assumptions. We prove that one may always find a representing closed 1-form having at most one zero. We introduce and study a generalization cat(X, ξ) of the notion of Lusternik Schnirelman category, depending on a topological space X and a 1-dimensional real cohomology class ξ ∈ H1(X;R)....
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ژورنال
عنوان ژورنال: Topology and its Applications
سال: 2001
ISSN: 0166-8641
DOI: 10.1016/s0166-8641(00)00076-6