A survey of Nielsen periodic point theory (fixed n)

Philip Heath

Banach Center Publications (1999)

  • Volume: 49, Issue: 1, page 159-188
  • ISSN: 0137-6934

How to cite

top

Heath, Philip. "A survey of Nielsen periodic point theory (fixed n)." Banach Center Publications 49.1 (1999): 159-188. <http://eudml.org/doc/208957>.

@article{Heath1999,
author = {Heath, Philip},
journal = {Banach Center Publications},
keywords = {Nielsen number; fibred Nielsen theory},
language = {eng},
number = {1},
pages = {159-188},
title = {A survey of Nielsen periodic point theory (fixed n)},
url = {http://eudml.org/doc/208957},
volume = {49},
year = {1999},
}

TY - JOUR
AU - Heath, Philip
TI - A survey of Nielsen periodic point theory (fixed n)
JO - Banach Center Publications
PY - 1999
VL - 49
IS - 1
SP - 159
EP - 188
LA - eng
KW - Nielsen number; fibred Nielsen theory
UR - http://eudml.org/doc/208957
ER -

References

top
  1. [1] R. F. Brown, The Lefschetz Fixed Point Theorem, Scott, Foresman, and Company, 1970. 
  2. [2] O. Davey, E. L. Hart, and K. Trapp, Computation of Nielsen numbers for maps of closed surfaces, Trans. Amer. Math. Soc. 348 (1996), 3245-3266. Zbl0861.55003
  3. [3] B. Halpern, Periodic points on tori, Pacific J. Math. 83 (1979), 117-133. Zbl0438.58023
  4. [4] B. Halpern, Periodic points on the Klein bottle, never published. 
  5. [5] B. Halpern, Nielsen type numbers for periodic points, never published. 
  6. [6] E. L. Hart and E. C. Keppelmann, Explorations in Nielsen periodic point theory for the double torus, Topology Appl. 95 (1999), 1-30. Zbl1007.55002
  7. [7] P. R. Heath, Product formulae for Nielsen numbers of fibre maps, Pacific J. Math. 117 (1985), 267-289. Zbl0571.55002
  8. [8] P. R. Heath, A Nielsen type number for fibre-preserving maps, Topology Appl. 53 (1993), 19-35. Zbl0789.55003
  9. [9] P. R. Heath, Relating relative, fibred and absolute Nielsen numbers of periodic points, Talk given at the AMS meeting in Baton Rouge, Louisiana, April 19-21, 1996, special session on 'Fixed point theory and dynamical systems' 
  10. [10] P. R. Heath, Nielsen type numbers for fibre preserving maps, coincidences of fibre preserving maps, and for periodic points of fibre preserving maps, C. R. Math. 14 (1992), 25-30. Zbl0752.55001
  11. [11] P. R. Heath and E. Keppelmann, Fibre techniques in Nielsen periodic point theory on nil and solvmanifolds, C. R. Math. 16 (1994), 229-234. Zbl0834.55004
  12. [12] P. R. Heath and E. Keppelmann, Fibre techniques in Nielsen periodic point theory on nil and solvmanifolds I, Topology Appl. 76 (1997), 217-247. Zbl0881.55002
  13. [13] P. R. Heath and E. Keppelmann, Fibre techniques in Nielsen periodic point theory on nil and solvmanifolds II, to appear in Topology Appl. Zbl0953.55001
  14. [14] P. R. Heath, E. Keppelmann, and P. Wong, Addition formulae for Nielsen numbers and for Nielsen type numbers of fibre preserving maps, Topology Appl. 67 (1995), 133-157. Zbl0845.55004
  15. [15] P. R. Heath, R. Piccinini, and C. You, Nielsen type numbers for periodic points I, in: B. Jiang (ed.), Topological Fixed Point Theory and Applications, Lecture Notes in Math. 1411, Springer, Berlin, 1989. Zbl0689.55006
  16. [16] P. R. Heath, H. Schirmer, and C. You, Nielsen type numbers for periodic points on nonconnected spaces, Topology Appl. 63 (1995), 97-116. Zbl0827.55001
  17. [17] P. R. Heath, H. Schirmer, and C. You, Nielsen type numbers for periodic points on pairs of spaces, Topology Appl. 63 (1995), 117-138. Zbl0827.55002
  18. [18] P. R. Heath and C. You, Nielsen type numbers for periodic points II, Topology Appl. 43 (1992), 219-236. Zbl0744.55001
  19. [19] P. R. Heath and X. Zhao, Periodic points on the complement, to appear in Topology Appl. Zbl0948.55002
  20. [20] B. Jiang, Lectures on Nielsen Fixed Point Theory, Contemp. Math. 14, Amer. Math. Soc., Providence, 1983. Zbl0512.55003
  21. [21] B. Jiang, Applications of the Nielsen theory to dynamics, these proceedings. 
  22. [22] E. Keppelmann, Periodic points on nilmanifolds and solvmanifolds, Pacific J. Math. 164 (1985), 105-128. Zbl0795.55002
  23. [23] E. Keppelmann and C. McCord, The Anosov theorem for exponential solvmanifolds, Pacific J. Math. 170 (1995), 143-159. Zbl0856.55003
  24. [24] C. McCord, Nielsen numbers and Lefschetz numbers on solvmanifolds, Pacific J. Math. 147 (1991), 153-164. Zbl0666.55002
  25. [25] H. Schirmer, A relative Nielsen number, Pacific J. Math. 122 (1986), 459-473. Zbl0553.55001
  26. [26] H. Schirmer, A survey of relative fixed point theory, in: Nielsen Theory and Dynamical Systems (Mt. Holyoke, 1992), Contemp. Math. 152, 1993, 291-3309. 
  27. [27] P. Wong, Equivariant Nielsen numbers, Pacific J. Math. 159 (1993), 153-175. Zbl0739.55001
  28. [28] P. Wong, Fixed points on pairs of nilmanifolds, Topology Appl. 62 (1995), 173-179. Zbl0819.55002
  29. [29] C. You, A note on periodic points on tori, preprint. 
  30. [30] C. You, The least number of periodic points on tori, Adv. in Math. 24 (1995), 155-160. Zbl0833.55003
  31. [31] X. Zhao, A relative Nielsen number for the complement, in: Topological Fixed Point Theory and Applications (Tianjin, 1998), Lecture Notes in Math. 1411, Springer, 1989, 257-265. 

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.