On the ∗-product in kneading theory
Brucks, Karen ; Galeeva, R. ; Mumbrú, P. ; Rockmore, D. ; Tresser, Charles
Fundamenta Mathematicae, Tome 154 (1997), p. 189-209 / Harvested from The Polish Digital Mathematics Library

We discuss a generalization of the *-product in kneading theory to maps with an arbitrary finite number of turning points. This is based on an investigation of the factorization of permutations into products of permutations with some special properties relevant for dynamics on the unit interval.

Publié le : 1997-01-01
EUDML-ID : urn:eudml:doc:212207
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     title = {On the *-product in kneading theory},
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     volume = {154},
     year = {1997},
     pages = {189-209},
     zbl = {0880.54025},
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Brucks, Karen; Galeeva, R.; Mumbrú, P.; Rockmore, D.; Tresser, Charles. On the ∗-product in kneading theory. Fundamenta Mathematicae, Tome 154 (1997) pp. 189-209. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-fmv152i3p189bwm/

[00000] [BORT] 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. | Zbl 0847.58019

[00001] [BDi] D. Bayer and P. Diaconis, Trailing the dovetail shuffle to its lair, Ann. Appl. Probab. 2 (1992), 294-313. | Zbl 0757.60003

[00002] [Be] C. Bernhardt, Simple permutations with order a power of two, Ergodic Theory Dynam. Systems 4 (1984), 179-186. | Zbl 0537.28008

[00003] [Bl] L. Block, Simple periodic orbits of mappings of the interval, Trans. Amer. Math. Soc. 254 (1979), 391-398. | Zbl 0386.54025

[00004] [CEc] P. Collet and J. P. Eckmann, Iterated Maps of the Interval as Dynamical Systems, Birkhäuser, Boston, 1980.

[00005] [CTr] P. Coullet et C. Tresser, Itérations d'endomorphismes et groupe de renormalisation, J. Phys. C 5 (1978), 25-28. | Zbl 0402.54046

[00006] [DGMT] 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. | Zbl 0909.54013

[00007] [DGP] 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. | Zbl 0416.28012

[00008] [DRSS] P. Doyle, D. Rockmore, V. Srimurthy and T. Sundquist, The turning point algebra, in preparation.

[00009] [Fe1] M. J. Feigenbaum, Quantitative universality for a class of non-linear transformations, J. Statist. Phys. 19 (1978), 25-52. | Zbl 0509.58037

[00010] [Fe2] M. J. Feigenbaum, The universal metric properties of non-linear transformations, J. Statist. Phys. 21 (1979), 669-706. | Zbl 0515.58028

[00011] [LMu1] 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.

[00012] [LMu2] J. Llibre and P. Mumbrú, Extending the *-product operator, in: Proceedings of ECIT 89, World Scientific, River Edge, N.J., 1991, 199-214. | Zbl 1026.37503

[00013] [JR] 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. | Zbl 0437.58017

[00014] [MSt] W. de Melo and S. van Strien, One Dimensional Dynamics, Ergeb. Math. Grenzgeb. (3) 25, Springer, Berlin, 1993.

[00015] [MSS] 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. | Zbl 0259.26003

[00016] [MTh] J. Milnor and W. Thurston, On iterated maps of the interval, in: Lecture Notes in Math. 1342, Springer, 1988, 465-563.

[00017] [Mi] 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. | Zbl 0414.34015

[00018] [MNi] M. Misiurewicz and Z. Nitecki, Combinatorial patterns for maps of the interval, Mem. Amer. Math. Soc. 456 (1991). | Zbl 0745.58019

[00019] [Mu] P. Mumbrú, Estructura Periòdica i Entropia Topològica de les Aplicacions Bimodals, Ph.D., Universitat Autònoma de Barcelona, 1987.

[00020] [My] P. J. Myrberg, Iteration der reellen Polynome zweiten Grades, Ann. Acad. Sci. Fenn. Ser. A I 256 (1958), 268 (1959) and 336 (1963).

[00021] [PTT] 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.

[00022] [So] L. Solomon, A Mackey formula in the group ring of a Coxeter group, J. Algebra 41 (1976), 255-264.

[00023] [TCo] C. Tresser et P. Coullet, Itérations d'endomorphismes et groupe de renormalisation, C. R. Acad. Sci. Paris Sér. A 287 (1978), 577-580. | Zbl 0402.54046