On the *-product in kneading theory

Fundamenta Mathematicae

Volumn 152, Issue 3, 1997, Pages 189-209

  Brucks, K ^a   Galeeva, R ^d   Mumbru P ^b   Rockmore, D ^e   Tresser, C ^c  

^a UNIVERSITY OF WISCONSIN MILWAUKEE   (United States)

^b UNIVERSITY OF BARCELONA   (Spain)

^c IBM T J WATSON RESEARCH CENTER   (United States)

^d UNIVERSITÉ DE LYON   (France)

^e DARTMOUTH COLLEGE   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000849372     PISSN: 00162736     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (24)

1. H. Bass, M. V. Otero-Espinar, D. Rockmore and C. Tresser, Cyclic Renormalization and Automorphism Groups of Rooted Trees, Lecture Notes in Math. 1621, Springer, 1995.
2. D. Bayer and P. Diaconis, Trailing the dovetail shuffle to its lair, Ann. Appl. Probab. 2 (1992), 294-313.
3. C. Bernhardt, Simple permutations with order a power of two, Ergodic Theory Dynam. Systems 4 (1984), 179-186.
4. L. Block, Simple periodic orbits of mappings of the interval, Trans. Amer. Math. Soc. 254 (1979), 391-398.
5. P. Collet and J. P. Eckmann, Iterated Maps of the Interval as Dynamical Systems, Birkhäuser, Boston, 1980.
6. P. Coullet et C. Tresser, Itérations d'endomorphismes et groupe de renormalisation, J. Phys. C 5 (1978), 25-28.
7. S. P. Dawson, R. Galeeva, J. Milnor and C. Tresser, A monotonicity conjecture for real cubic maps, in: Real and Complex Dynamical Systems, B. Branner and P. Hjorth (eds.), Kluwer, Dordrecht, 1995.
8. B. Derrida, A. Gervois, and Y. Pomeau, Iteration of endomorphisms on the real axis and representation of numbers, Ann. Inst. H. Poincaré Sect. A 29 (1978), 305-356.
9. P. Doyle, D. Rockmore, V. Srimurthy and T. Sundquist, The turning point algebra, in preparation.
10. M. J. Feigenbaum, Quantitative universality for a class of non-linear transformations, J. Statist. Phys. 19 (1978), 25-52.
11. -, The universal metric properties of non-linear transformations, ibid. 21 (1979), 669-706.
12. J. Llibre and P. Mumbrú, Renormalisation and periodic structure for bimodal maps, in: Proceedings of ECIT 87, World Scientific, Teaneck, N.J., 1989, 253-262.
13. -, -, Extending the *-product operator, in: Proceedings of ECIT 89, World Scientific, River Edge, N.J., 1991, 199-214.
14. L. Jonker and D. Rand, The periodic orbits and entropy of certain maps of the unit interval, J. London Math. Soc. (2) 22 (1980), 175-181.
15. W. de Melo and S. van Strien, One Dimensional Dynamics, Ergeb. Math. Grenzgeb. (3) 25, Springer, Berlin, 1993.
16. N. Metropolis, M. L. Stein and P. R. Stein, On finite limit sets for transformations on the unit interval, J. Combin. Theory Ser. A 15 (1973), 25-44.
17. J. Milnor and W. Thurston, On iterated maps of the interval, in: Lecture Notes in Math. 1342, Springer, 1988, 465-563.
18. C. Mira, Accumulations de bifurcations et "structures boîtes emboîtées" dans les récurrences et transformations ponctuelles, in: Internationale Konferenz über nichtlineare Schwingungen (Berlin, 1975), Band I, Teil 2, Akademie-Verlag, Berlin, 1977, 80-93.
19. M. Misiurewicz and Z. Nitecki, Combinatorial patterns for maps of the interval, Mem. Amer. Math. Soc. 456 (1991).
20. P. Mumbrú, Estructura Periòdica i Entropia Topològica de les Aplicacions Bimodals, Ph.D., Universitat Autonoma de Barcelona, 1987.
21. P. J. Myrberg, Iteration der reellen Polynome zweiten Grades, Ann. Acad. Sci. Fenn. Ser. A I 256 (1958), 268 (1959) and 336 (1963).
22. I. Procaccia, S. Thomae and C. Tresser, First return maps as a unified renormalization scheme for dynamical systems, Phys. Rev. A 35 (1987), 1884-1900.
23. L. Solomon, A Mackey formula in the group ring of a Coxeter group, J. Algebra 41 (1976), 255-264.
24. C. Tresser et P. Coullet, Itérations d'endomorphismes et groupe de renormalisation, C. R. Acad. Sci. Paris Sér. A 287 (1978), 577-580.