Skip to main content

More about Nielsen Theories and Their Applications

  • Chapter
Book cover Handbook of Topological Fixed Point Theory

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. J. Andres, A nontrivial example of application of the Nielsen fixed-point theory to differential systems: Problem of Jean Leray, Proc. Amer. Math. Soc. 128 (2000), 2921–2931.

    Article  MATH  MathSciNet  Google Scholar 

  2. J. Andres and L. Górniewicz, Topological Fixed Point Principles for Boundary Value Problems, Kluwer.

    Google Scholar 

  3. A. Borisovich, Z. Kucharski and W. Marzantowicz, A multiplicity result for a system of real integral equations by use of the Nielsen number, Banach Center Publ. 49 (1999), 9–18.

    MathSciNet  Google Scholar 

  4. R. Brown, The Lefschetz Fixed Point Theorem (1971), Scott, Foresman.

    Google Scholar 

  5. _____, Fixed point theory, History of Topology, Elsevier, 1999, pp. 271–299.

    Google Scholar 

  6. _____, A Topological Introduction to Nonlinear Analysis, Second Edition, Birkhäuser, 2004.

    Google Scholar 

  7. _____, Topological identification of multiple solutions to parametrized nonlinear equations, Pacific J. Math. 131 (1988), 51–69.

    Google Scholar 

  8. R. Brown and R. Greene, An interior fixed point property of the disc, Amer. Math. Monthly 101 (1994), 39–48.

    Article  MathSciNet  MATH  Google Scholar 

  9. R. Brown, R. Greene and H. Schirmer, Fixed points of map extensions, Springer Lecture Notes in Math. 1411 (1989), 24–45.

    MathSciNet  Google Scholar 

  10. R. Brown and P. Zezza, Multiple local solutions to nonlinear control processes, J. Optim. Theory Appl. 67 (1990), 463–485.

    Article  MathSciNet  MATH  Google Scholar 

  11. F. Cardona and P. Wong, The relative Reidemeister number of fiber map pairs, Topol. Methods Nonlinear Anal. 21 (2003), 131–145.

    MathSciNet  MATH  Google Scholar 

  12. H. Cho and M. Woo, A relative mod (H,K) Nielsen number, J. Korean Math. Soc. 32 (1995), 371–387.

    MathSciNet  MATH  Google Scholar 

  13. D. Chun, C. Jang and S. Lee, Estimation of the number of common essential fixed point classes, Bull. Honam Math. Soc. 13 (1996), 157–163.

    MathSciNet  MATH  Google Scholar 

  14. D. Dimovski and R. Geoghegan, One-parameter fixed point theory, Forum Math. 2 (1990), 125–154.

    Article  MathSciNet  MATH  Google Scholar 

  15. Z. Dzedzej, Fixed point index theory for a class of nonacyclic multivalued mappings, Diss. Math. 253 (1985).

    Google Scholar 

  16. E. Fadell and S. Husseini, Local fixed point index theory for non simply connected manifolds, Illinois J. Math. 25 (1981), 673–699.

    MathSciNet  MATH  Google Scholar 

  17. _____, The Nielsen number on surfaces, Contemp. Math. 21 (1983), 59–98.

    MathSciNet  MATH  Google Scholar 

  18. J. Fares and E. Hart, A generalized Lefschetz number for the local Nielsen fixed point theory, Topology Appl. 59 (1994), 1–23.

    Article  MathSciNet  MATH  Google Scholar 

  19. M. Fečkan, Multiple solutions of nonlinear equations via Nielsen fixed-point theory: a survey, Nonlinear Analysis in Geometry and Topology, Hadronic Press, 2000, pp. 77–97.

    Google Scholar 

  20. _____, Nielsen fixed point theory and nonlinear equations, J. Differential Equations 106 (1993), 312–331.

    Article  MathSciNet  MATH  Google Scholar 

  21. _____, Parametrized singularly perturbed boundary value problems, J. Math. Anal. Appl. 188 (1994), 417–425.

    Article  MathSciNet  MATH  Google Scholar 

  22. _____, Multiple periodic solutions of small vector fields on differential equations, J. Differential Equations 113 (1994), 189–200.

    Article  MathSciNet  MATH  Google Scholar 

  23. _____, Parametrized singular boundary value problems, J. Math. Anal. Appl. 188 (1994), 426–435.

    Article  MathSciNet  MATH  Google Scholar 

  24. _____, Differential equations with nonlinear boundary conditions, Proc. Amer. Math. Soc. 121 (1994), 103–111.

    Article  MathSciNet  MATH  Google Scholar 

  25. _____, Note on weakly inward mappings, Ann. Polon. Math. 63 (1996), 1–5.

    MathSciNet  MATH  Google Scholar 

  26. _____, The interaction of linear boundary value and nonlinear functional conditions, Ann. Polon. Math. 58 (1993), 103–111.

    Google Scholar 

  27. A. Fel'shtyn, Dynamical zeta functions, Nielsen theory and Reidemeister torsion, Mem. Amer. Math. Soc. 699 (2000).

    Google Scholar 

  28. D. Ferrario and D. Goncalves, Homeomorphisms of surfaces locally may not have the Wecken property, XI Brazilian Topology Meeting, 2000, pp. 1–9.

    Google Scholar 

  29. M. Furi, P. Nistri, M. Pera and P. Zezza, Topological methods for the global controllability of non-linear systems, J. Optim. Theory Appl. 45 (1985), 231–256.

    Article  MathSciNet  MATH  Google Scholar 

  30. R. Geoghegan, Nielsen fixed point theory, Handbook of Geometric Topology, 2002, pp. 499–521.

    Google Scholar 

  31. D. Gonçalves, Braid groups and Wecken pairs, Contemp. Math. 72 (1986), 89–97.

    Google Scholar 

  32. L. Górniewicz, Topological Fixed Point Theory of Multivalued Mappings, Kluwer Academic Publishers, 1999.

    Google Scholar 

  33. L. Górniewicz, A. Granas and W. Kryszewski, Sur la méthode de l'homotopie dans la théorie des points fixes pour les applications multivoques, 1, C. R. Acad. Sci. Paris Sèr. I 307 (1988), 489–492.

    Google Scholar 

  34. _____, Sur la méthode de l'homotopie dans la théorie des points fixes pour les applications multivoques, 2, C. R. Acad. Sci. Paris Sèr. I 308 (1989), 449–452.

    Google Scholar 

  35. A. Granas, The Leray-Shauder index and the fixed point theory for arbitrary ANRs, Bull. Soc. Math. France 100 (1972), 209–228.

    MATH  MathSciNet  Google Scholar 

  36. A. Granas and J. Dugundji, Fixed Point Theory, Springer, 2003.

    Google Scholar 

  37. R. Greene and H. Schirmer, Smooth realization of relative Nielsen numbers, Topology Appl. 66 (1995), 93–100.

    Article  MathSciNet  MATH  Google Scholar 

  38. E. Hart, Local Nielsen fixed point theory and the local generalized H-Lefschetz number, Contemp. Math. 152 (1993), 177–182.

    MATH  MathSciNet  Google Scholar 

  39. _____, Computation of the local generalized H-Lefschetz number, Topology Appl. 61 (1995), 115–135.

    Article  MATH  MathSciNet  Google Scholar 

  40. G. Hirsch, Detérmination d'un nombre minimum de points fixes pour certaines représentations, Bull. Sci. Math. 64 (1940), 45–55.

    MATH  MathSciNet  Google Scholar 

  41. N. Ivanov, Entropy and the Nielsen numbers, Soviet Math. Dokl. 26 (1982), 63–66.

    MATH  Google Scholar 

  42. J. Jezierski, The Nielsen relation for multivalued maps, Serdica 13 (1987), 174–181.

    MATH  MathSciNet  Google Scholar 

  43. B. Jiang, Fixed point classes from a differentiable viewpoint, Springer Lecture Notes in Math. 886 (1981), 163–170.

    MATH  Google Scholar 

  44. _____, Fixed points and braids II, Math. Ann. 272 (1985), 249–256.

    Article  MATH  MathSciNet  Google Scholar 

  45. _____, Nielsen theory for periodic orbits and applications to dynamical systems, Contemp. Math. 152 (1993), 183–202.

    MATH  Google Scholar 

  46. _____, Applications of Nielsen theory to dynamics, Banach Center Publications 49 (1999), 203–221.

    MATH  Google Scholar 

  47. _____, Lectures on Nielsen fixed point theory, Contemp. Math. 14 (1983).

    Google Scholar 

  48. _____, Estimation of the number of periodic orbits, Pacific J. Math. 172 (1996), 151–185.

    MATH  MathSciNet  Google Scholar 

  49. B. Jiang and J. Guo, Fixed points of surface diffeomorphisms, Pacific J. Math. 160 (1993), 67–89.

    MathSciNet  MATH  Google Scholar 

  50. W. Kryszewski and D. Miklaszewski, The Nielsen number of set-valued maps: An approximation approach, Serdica 15 (1989), 336–344.

    MathSciNet  MATH  Google Scholar 

  51. R. Leggett and L. Williams, Multiple positive fixed points of non-linear operators on ordered Banach spaces, Indiana Univ. Math. J. 28 (1979), 673–688.

    Article  MathSciNet  MATH  Google Scholar 

  52. J. Leray, Le theorie des points fixes et ses applications en analyse, Proc. Inter. Congress of Math., 1950 2 (1952), 202–208.

    MATH  MathSciNet  Google Scholar 

  53. _____, Théorie des pointes fixés: indice total et nombre de Lefschetz, Bull. Soc. Math. France 87 (1959), 221–233.

    MATH  MathSciNet  Google Scholar 

  54. J. Leray and J. Schauder, Topologie et equations fonctionnelles, Ann. Sci. École Norm. Sup. (4) 51 (1934), 45–78.

    MathSciNet  MATH  Google Scholar 

  55. S. Masih, On the fixed point index and Nielsen fixed point theorem for symmetric product mappings, Fund. Math. 102 (1979), 143–158.

    MATH  MathSciNet  Google Scholar 

  56. C. McCord, A Nielsen theory for intersection numbers, Fund. Math. 152 (1997), 117–150.

    MATH  MathSciNet  Google Scholar 

  57. _____, Wecken theorems for Nielsen intersection theory, Banach Center Publ. 49 (1999), 235–252.

    MATH  MathSciNet  Google Scholar 

  58. _____, The three faces of Nielsen: coincidences, intersections and preimages, Topology Appl. 103 (2000), 155–177.

    Article  MATH  MathSciNet  Google Scholar 

  59. D. McCord, An estimate of the Nielsen number and an example concerning the Lefschetz fixed point theorem, Pacific J. Math. 66 (1976), 195–203.

    MATH  MathSciNet  Google Scholar 

  60. D. Miklaszewski, A reduction of the Nielsen fixed point theorem for symmetric product maps to the Lefschetz theorem, Fund. Math. 135 (1990), 175–176.

    MATH  MathSciNet  Google Scholar 

  61. B. O'Neill, Induced homology homomorphisms for set-valued maps, Pacific J. Math. 7 (1957), 1179–1184.

    MATH  MathSciNet  Google Scholar 

  62. H. Schirmer, Nielsen theory of transversal fixed point sets, Fund. Math. 141 (1992), 31–59.

    MATH  MathSciNet  Google Scholar 

  63. _____, A relative Nielsen number, Pacific J. Math. 122 (1986), 459–473.

    MATH  MathSciNet  Google Scholar 

  64. _____, A Nielsen number for fixed points and near points of small multifunctions, Fund. Math. 88 (1975), 145–156.

    MATH  MathSciNet  Google Scholar 

  65. _____, Simplicial approximation of small multifunctions, Fund. Math. 84 (1974), 121–126.

    MATH  MathSciNet  Google Scholar 

  66. _____, An index and Nielsen number for n-valued multifunctions, Fund. Math. 124 (1984), 207–219.

    MATH  MathSciNet  Google Scholar 

  67. _____, Fix-finite approximations of n-valued multifunctions, Fund. Math. 121 (1984), 73–80.

    MATH  MathSciNet  Google Scholar 

  68. _____, A minimum theorem for n-valued multifunctions, Fund. Math. 126 (1985), 83–92.

    MATH  MathSciNet  Google Scholar 

  69. _____, A fixed point index for bimaps, Fund. Math. 134 (1990), 93–104.

    MATH  MathSciNet  Google Scholar 

  70. _____, The least number of fixed points of bimaps, Fund. Math. 137 (1991), 1–8.

    MATH  MathSciNet  Google Scholar 

  71. M. Shub and D. Sullivan, A remark on the Lefschetz fixed point formula for differentiable maps, Topology 13 (1974), 189–191.

    Article  MathSciNet  MATH  Google Scholar 

  72. K. Scholz, The Nielsen fixed point theory for non-compact spaces, Rocky Mountain J. Math. 4 (1974), 81–87.

    Article  MATH  MathSciNet  Google Scholar 

  73. S. Wang, General H-fixed point classes and their application, Beijing Daxue Xuebao (1982), 11–18.

    Google Scholar 

  74. P. Wong, A note on the local and extension Nielsen numbers, Topology Appl. 48 (1992), 207–213.

    Article  MATH  MathSciNet  Google Scholar 

  75. M. Woo and H. Cho, A relative modK Nielsen number, J. Korean Math. Soc. 29 (1992), 409–422.

    MathSciNet  MATH  Google Scholar 

  76. M. Woo and J. Kim, Note on a lower bound of Nielsen number, J. Korean Math. Soc. 29 (1992), 117–125.

    MathSciNet  MATH  Google Scholar 

  77. C. You, Fixed point classes of a fiber map, Pacific J. Math. 100 (1982), 217–241.

    MATH  MathSciNet  Google Scholar 

  78. X. Zhao, A new Nielsen type number for map extensions, Far East J. Math. Sci. 2 (1994), 17–26.

    MATH  MathSciNet  Google Scholar 

  79. _____, Estimation of the number of fixed points of map extensions, Acta Math. Sinica 8 (1992), 357–361.

    Article  MATH  MathSciNet  Google Scholar 

  80. _____, A relative Nielsen number for the complement, Springer Lecture Notes in Math. 1411 (1989), 189–199.

    Article  MATH  Google Scholar 

Download references

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2005 Springer

About this chapter

Cite this chapter

Brown, R.F. (2005). More about Nielsen Theories and Their Applications. In: Brown, R.F., Furi, M., Górniewicz, L., Jiang, B. (eds) Handbook of Topological Fixed Point Theory. Springer, Dordrecht. https://doi.org/10.1007/1-4020-3222-6_12

Download citation

Publish with us

Policies and ethics