Results 11 to 20 of about 245 (151)
On the Lefschetz Fixed Point Theorem [PDF]
, 2005 The abstract version of the Lefschetz fixed point theorem is proved which states the following: If \(X\) is a metric space and if \(X_0\subset X\) is such that \(X_0\) absorbs compact sets, \(f\:X\to X\) is a continuous map, \(f(X_0) \subset X_0\) and \(f/X_0\) is a Lefschetz map, then \(f\) is also (on \(X\)) a Lefschetz map. Here a continuous map \(f\
Lech Górniewicz
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A generalization of the Lefschetz fixed point theorem and detection of chaos [PDF]
Proceedings of the American Mathematical Society, 1999 We consider the problem of existence of fixed points of a continuous map f : X → X f:X\to X in (possibly) noninvariant subsets. A pair ( C , E ) (C,E) of subsets of X X induces a map f †
Roman Srzednicki
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A generalized Lefschetz fixed point theorem and symbolic dynamics in delay equations
Ergodic Theory and Dynamical Systems, 2002 We prove a generalized version of the Lefschetz fixed point theorem, and use it to obtain a variety of periodic and aperiodic solutions for differential delay equations; in particular, of the type \dot x(t) = f(x(t-1)). Here f:\mathbb R \to \mathbb R is odd and two-periodic, and we obtain both strictly periodic solutions and solutions periodic modulo a
Bernhard Lani‐Wayda, Roman Srzednicki
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A NOTE ON THE LEFSCHETZ FIXED POINT THEOREM FOR ADMISSIBLE SPACES [PDF]
Bulletin of the Korean Mathematical Society, 2005 A Hausdorff topological space \(X\) is said to be a \textit{Lefschetz space} provided that, for any compact continuous map \(f: X\to X\), the generalized Lefschetz number \(\Lambda(f)\) is defined and \(\Lambda(f)\neq 0\) implies that \(f\) has a fixed point. By \textit{G. Fournier} and \textit{A. Granas} [J. Math. Pures Appl., IX. Sér.
Ravi P. Agarwal, Donal O’Regan
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A Lefschetz fixed point theorem for multivalued maps of finite spaces [PDF]
Mathematische Zeitschrift, 2019 We prove a version of the Lefschetz fixed point theorem for multivalued maps $F:X\multimap X$ in which $X$ is a finite $T_0$ space.
Jonathan Ariel Barmak +2 more
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Lefschetz fixed point theorem for intersection homology
Commentarii Mathematici Helvetici, 1985 Es sei X eine kompakte orientierbare n-dimensionale topologische Mannigfaltigkeit. Für eine stetige Selbstabbildung \(f: X\to X\) liefert der klassische Fixpunktsatz von Lefschetz eine notwendige algebraisch- topologische Bedingung für die Existenz von Fixpunkten: Ist \(\Delta\) die Diagonale von \(X\times X\) und G(f) der Graph von f in \(X\times X\),
Mark Goresky, Robert MacPherson
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The equivariant Lefschetz fixed point theorem for proper cocompact G-manifolds [PDF]
, 2002 Suppose one is given a discrete group G, a cocompact proper G-manifold M, and a G-self-map f of M. Then we introduce the equivariant Lefschetz class of f, which is globally defined in terms of cellular chain complexes, and the local equivariant Lefschetz class of f, which is locally defined in terms of fixed point data.
Wolfgang Lueck, Jonathan Rosenberg
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A Lefschetz-type fixed point theorem [PDF]
Fundamenta Mathematicae, 1975 Lech Górniewicz
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On a homotopy converse to the Lefschetz fixed point theorem [PDF]
Pacific Journal of Mathematics, 1966 Robert F. Brown
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Generalized Lefschetz theorem and a fixed point index formula
Topology and its Applications, 1997 The Lefschetz fixed point theorem says that if the Lefschetz index \(\Lambda(f)\) of a continuous mapping \(f:X\to X\) from a finite polyhedron \(X\) into itself is non-zero, then \(f\) has a fixed point. Here, \(\Lambda(f)\) is defined as a sum \(\Lambda(f)=\sum_n (-1)^n\cdot \text{ tr}(h_n(f))\), where \(h_n(f)\) is a homomorphism of a \(Z\)-module \(
Roman Srzednicki
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