Abstract
Associated to an isolated periodic point of a continuous self map on a manifold is an invariant called the Lefschetz function. It is a formal power series which encapsulates the values of the Lefschetz index of the fixed point for all iterates of the map. We prove that for a homeomorphism of a manifold of dimension at least three any formal power series with integer coefficients and leading term 1 can be realized as the Lefschetz function of a fixed point.
Keywords
- Periodic Orbit
- Periodic Point
- Boundary Component
- Formal Power Series
- Infinite Product
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References
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D. Fried, Periodic Points and Twisted Coefficients, in Geometric Dynamics, Proceedings Rio de Janeiro 1981, Springer Lecture Notes in Math. 1007, 261–293.
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© 1989 Springer-Verlag
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Franks, J., Fried, D. (1989). The lefschetz function of a point. In: Jiang, B. (eds) Topological Fixed Point Theory and Applications. Lecture Notes in Mathematics, vol 1411. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0086443
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DOI: https://doi.org/10.1007/BFb0086443
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Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-51932-4
Online ISBN: 978-3-540-46862-2
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