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Discrete and Continuous Dynamical Systems - Series A (DCDS-A)
 

Typical points for one-parameter families of piecewise expanding maps of the interval
Pages: 877 - 911, Issue 3, November 2011

doi:10.3934/dcds.2011.31.877      Abstract        References        Full text (600.1K)           Related Articles

Daniel Schnellmann - Ecole Normale Supérieure, Départment de mathématiques et applications (DMA), 45 rue d’Ulm 75230 Paris cedex 05, France (email)

1 V. Baladi, On the susceptibility function of piecewise expanding interval maps, Comm. Math. Phys., 275 (2007), 839-859.       
2 V. Baladi and D. Smania, Linear response formula for piecewise expanding unimodal maps, Nonlinearity, 21 (2008), 677-711.       
3 V. Baladi and D. Smania, Smooth deformation of piecewise expanding unimodal maps, Discrete Contin. Dyn. Syst., 23 (2009), 685-703.       
4 M. Benedicks and L. Carleson, On iterations of $1-ax^2$ on $(-1,1)$, Ann. of Math. (2), 122 (1985), 1-25.       
5 M. Björklund and D. Schnellmann, Almost sure equidistribution in expansive families, Indag. Math. (N.S.), 20 (2009), 167-177.       
6 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.       
7 H. Bruin, For almost every tent-map, the turning point is typical, Fund. Math., 155 (1998), 215-235.       
8 P. Collet and J.-P. Eckmann, "Iterated Maps on the Interval as Dynamical Systems," Birkhäuser, Boston, 1980.
9 B. Faller and C.-E. Pfister, A point is normal for almost all maps $\beta x+\alpha\mod1$ or generalized $\beta$-transformations, Ergodic Theory Dynam. Systems, 29 (2009), 1529-1547.       
10 A. Lasota and J. A. Yorke, On the existence of invariant measures for piecewise monotonic transformations, Trans. Amer. Math. Soc., 186 (1973), 481-488.       
11 T.-Y. Li and J. A. Yorke, Ergodic transformations from an interval into itself, Trans. Amer. Math. Soc., 235 (1978), 183-192.       
12 P. Mattila, "Geometry of Sets and Measures in Euclidean Spaces (Cambridge studies in advanced mathematics)," Cambridge University Press, Cambridge, 1995.
13 M. Misiurewicz and E. Visinescu, Kneading sequences of skew tent maps, Ann. Inst. H. Poincaré Probab. Statist., 27 (1991), 125-140.       
14 V. A. Rohlin, Exact endomorphisms of a Lebesgue space, (Russian) Izv. Akad. Nauk SSSR Ser. Mat., 25 (1961), 499-530, (English) Amer. Math. Soc. Transl. Ser. 2, 39 (1964), 1-36.       
15 J. Schmeling, Symbolic dynamics for $\beta$-shifts and self-normal numbers, Ergodic Theory Dynam. Systems, 17 (1997), 675-694.       
16 M. Tsujii, Lyapunov exponents in families of one-dimensional dynamical systems, Invent. Math., 111 (1993), 113-137.       
17 G. Wagner, The ergodic behaviour of piecewise monotonic transformations, Z. Wahrsch. Verw. Gebiete, 46 (1979), 317-324.       
18 S. Wong, Some metric properties of piecewise monotonic mappings of the unit interval, Trans. Amer. Math. Soc., 246 (1978), 493-500.       

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