Abstract and Applied Analysis

Periods for holomorphic maps via Lefschetz numbers

Jaume Llibre and Michael Todd

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Abstract

We characterise the set of fixed points of a class of holomorphic maps on complex manifolds with a prescribed homology. Our main tool is the Lefschetz number and the action of maps on the first homology group.

Article information

Source
Abstr. Appl. Anal., Volume 2005, Number 6 (2005), 575-579.

Dates
First available in Project Euclid: 3 October 2005

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1128345938

Digital Object Identifier
doi:10.1155/AAA.2005.575

Mathematical Reviews number (MathSciNet)
MR2202948

Zentralblatt MATH identifier
1112.58010

Citation

Llibre, Jaume; Todd, Michael. Periods for holomorphic maps via Lefschetz numbers. Abstr. Appl. Anal. 2005 (2005), no. 6, 575--579. doi:10.1155/AAA.2005.575. https://projecteuclid.org/euclid.aaa/1128345938


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References

  • R. F. Brown, The Lefschetz Fixed Point Theorem, Scott, Foresman and Company, Illinois, 1971.
  • C. J. Earle and R. S. Hamilton, A fixed point theorem for holomorphic mappings, Global Analysis (Proc. Sympos. Pure Math., Vol. 16, Berkeley, Calif, 1968), American Mathematical Society, Rhode Island, 1970, pp. 61--65.
  • N. Fagella and J. Llibre, Periodic points of holomorphic maps via Lefschetz numbers, Trans. Amer. Math. Soc. 352 (2000), no. 10, 4711--4730.
  • L. A. Harris, Fixed points of holomorphic mappings for domains in Banach spaces, Abstr. Appl. Anal. 2003 (2003), no. 5, 261--274.
  • J. X. Hou, Periodic points of analytical dynamical systems on hyperbolic Riemann surfaces, Acta Sci. Natur. Univ. Sunyatseni 1988 (1988), no. 1, 28--33.
  • J. Milnor, Notes on dynamical systems, www.math.sunysb.edu/$\sim$jack/DYNOTES/.
  • --------, Dynamics in One Complex Variable, 2nd ed., Friedr. Vieweg & Sohn, Braunschweig, 1999.
  • G. Pick, Über einer eigenschaft der konformen abbildung kreisförmiger berieche, Math. Ann. 77 (1916), 1--6 (German).
  • J. W. Vick, Homology Theory, 2nd ed., Graduate Texts in Mathematics, vol. 145, Springer-Verlag, New York, 1994.