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1997 | 152 | 3 | 189-209
Tytuł artykułu

On the ∗-product in kneading theory

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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.
Słowa kluczowe
Kategorie tematyczne
Rocznik
Tom
152
Numer
3
Strony
189-209
Opis fizyczny
Daty
wydano
1997
otrzymano
1995-03-02
poprawiono
1996-07-15
Twórcy
autor
  • Department of Mathematical Sciences, University of Wisconsin-Milwaukee, Milwaukee, Wisconsin 53201, U.S.A., kmbrucks@csd.uwm.edu
autor
autor
  • Department of Mathematics, Facultat de Matemàtiques, Departament de Matemática, Aplicada i Anàlisi, Universitat de Barcelona Gran Via, 585 08071 Barcelona, Spain, mumbru@cerber.amt.ub.es
autor
Bibliografia
  • [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.
  • [BDi] D. Bayer and P. Diaconis, Trailing the dovetail shuffle to its lair, Ann. Appl. Probab. 2 (1992), 294-313.
  • [Be] C. Bernhardt, Simple permutations with order a power of two, Ergodic Theory Dynam. Systems 4 (1984), 179-186.
  • [Bl] L. Block, Simple periodic orbits of mappings of the interval, Trans. Amer. Math. Soc. 254 (1979), 391-398.
  • [CEc] P. Collet and J. P. Eckmann, Iterated Maps of the Interval as Dynamical Systems, Birkhäuser, Boston, 1980.
  • [CTr] P. Coullet et C. Tresser, Itérations d'endomorphismes et groupe de renormalisation, J. Phys. C 5 (1978), 25-28.
  • [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.
  • [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.
  • [DRSS] P. Doyle, D. Rockmore, V. Srimurthy and T. Sundquist, The turning point algebra, in preparation.
  • [Fe1] M. J. Feigenbaum, Quantitative universality for a class of non-linear transformations, J. Statist. Phys. 19 (1978), 25-52.
  • [Fe2] M. J. Feigenbaum, The universal metric properties of non-linear transformations, J. Statist. Phys. 21 (1979), 669-706.
  • [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.
  • [LMu2] J. Llibre and P. Mumbrú, Extending the *-product operator, in: Proceedings of ECIT 89, World Scientific, River Edge, N.J., 1991, 199-214.
  • [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.
  • [MSt] W. de Melo and S. van Strien, One Dimensional Dynamics, Ergeb. Math. Grenzgeb. (3) 25, Springer, Berlin, 1993.
  • [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.
  • [MTh] J. Milnor and W. Thurston, On iterated maps of the interval, in: Lecture Notes in Math. 1342, Springer, 1988, 465-563.
  • [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.
  • [MNi] M. Misiurewicz and Z. Nitecki, Combinatorial patterns for maps of the interval, Mem. Amer. Math. Soc. 456 (1991).
  • [Mu] P. Mumbrú, Estructura Periòdica i Entropia Topològica de les Aplicacions Bimodals, Ph.D., Universitat Autònoma de Barcelona, 1987.
  • [My] P. J. Myrberg, Iteration der reellen Polynome zweiten Grades, Ann. Acad. Sci. Fenn. Ser. A I 256 (1958), 268 (1959) and 336 (1963).
  • [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.
  • [So] L. Solomon, A Mackey formula in the group ring of a Coxeter group, J. Algebra 41 (1976), 255-264.
  • [TCo] C. Tresser et P. Coullet, Itérations d'endomorphismes et groupe de renormalisation, C. R. Acad. Sci. Paris Sér. A 287 (1978), 577-580.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-fmv152i3p189bwm
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