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2000 | 165 | 2 | 95-123
Tytuł artykułu

Trajectory of the turning point is dense for a co-σ-porous set of tent maps

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
It is known that for almost every (with respect to Lebesgue measure) a ∈ [√2,2] the forward trajectory of the turning point of the tent map $T_a$ with slope a is dense in the interval of transitivity of $T_a$. We prove that the complement of this set of parameters of full measure is σ-porous.
Słowa kluczowe
Rocznik
Tom
165
Numer
2
Strony
95-123
Opis fizyczny
Daty
wydano
2000
otrzymano
1998-07-10
Twórcy
autor
  • Department of Mathematical Sciences, University of Wisconsin at Milwaukee, Milwaukee, WI 53201, U.S.A., kmbrucks@csd.uwm.edu
  • Department of Analysis, Eötvös Loránd University, Múzeum krt. 6-8, H-1088 Budapest, Hungary, buczo@cs.elte.hu
Bibliografia
  • [1] L. Block and W. A. Coppel, Dynamics in One Dimension, Lecture Notes in Math. 1513, Springer, New York, 1992.
  • [2] K. Brucks, B. Diamond, M. V. Otero-Espinar and C. Tresser, Dense orbits of critical points for the tent map, in: Contemp. Math. 117, Amer. Math. Soc., 1991, 57-61.
  • [3] K. Brucks and M. Misiurewicz, The trajectory of the turning point is dense for almost all tent maps, Ergodic Theory Dynam. Systems 16 (1996), 1173-1183.
  • [4] H. Bruin, Invariant measures of interval maps, Ph.D. thesis, Delft, 1994.
  • [5] H. Bruin, Combinatorics of the kneading map, Internat. J. Bifur. Chaos Appl. Sci. Engrg. 5 (1995), 1339-1349.
  • [6] H. Bruin, Quasi-symmetry of conjugacies between interval maps, Nonlinearity 9 (1996), 1191-1207.
  • [7] H. Bruin, Topological conditions for the existence of absorbing Cantor sets, Trans. Amer. Math. Soc. 350 (1998), 2229-2263.
  • [8] H. Bruin, For almost every tent map, the turning point is typical, Fund. Math. 155 (1998), 215-235.
  • [9] F. Hofbauer, The topological entropy of the transformation x ↦ ax(1-x), Monatsh. Math. 90 (1980), 117-141.
  • [10] F. Hofbauer and G. Keller, Quadratic maps without asymptotic measure, Comm. Math. Phys. 127 (1990), 319-337.
  • [11] W. de Melo and S. van Strien, One-Dimensional Dynamics, Springer, New York, 1993.
  • [12] D. Preiss and L. Zajíček, Fréchet differentiation of convex functions in a Banach space with a separable dual, Proc. Amer. Math. Soc. 91 (1984), 202-204.
  • [13] D. L. Renfro, On some various porosity notions, preprint, 1995.
  • [14] D. Sands, Topological conditions for positive Lyapunov exponent in unimodal maps, Ph.D. thesis, Cambridge, 1994.
  • [15] S. van Strien, Smooth dynamics on the interval, in: New Directions in Dynamical Systems, London Math. Soc. Lecture Note Ser. 127, Cambridge Univ. Press, Cambridge, 1988, 57-119.
  • [16] B. S. Thomson, Real Functions, Lecture Notes in Math. 1170, Springer, New York, 1985.
  • [17] L. Zajíček, Porosity and σ-porosity, Real Anal. Exchange 13 (1987-88), 314-347.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-fmv165i2p95bwm
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