August  2013, 33(8): 3741-3751. doi: 10.3934/dcds.2013.33.3741

A footnote on expanding maps

1. 

Dipartimento di Matematica, II Università di Roma (Tor Vergata), Via della Ricerca Scientifica, 00133 Roma

Received  June 2012 Revised  October 2012 Published  January 2013

I introduce Banach spaces on which it is possible to precisely characterize the spectrum of the transfer operator associated to a piecewise expanding map with Hölder weight.
Citation: Carlangelo Liverani. A footnote on expanding maps. Discrete & Continuous Dynamical Systems, 2013, 33 (8) : 3741-3751. doi: 10.3934/dcds.2013.33.3741
References:
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Dynamical Systems. Part II, 185-237, Pubbl. Cent. Ric. Mat. Ennio Giorgi, Scuola Norm. Sup., Pisa, (2003).  Google Scholar

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Ann. of Math. (2), 159 (2004), 1275-1312. doi: 10.4007/annals.2004.159.1275.  Google Scholar

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Israel J. Math., 116 (2000), 223-248. doi: 10.1007/BF02773219.  Google Scholar

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show all references

References:
[1]

V. Araujo, S. Galatolo and M.-J. Pacifico, Decay of correlations for maps with uniformly contracting fibers and logarithm law for singular hyperbolic attractors,, Preprint , ().   Google Scholar

[2]

16 of Advanced Series in Nonlinear Dynamics. World Scientific, Singapore, 2000. doi: 10.1142/9789812813633.  Google Scholar

[3]

Algebraic and Topological Dynamics, 123-135, Contemp. Math., 385, Amer. Math. Soc., Providence, RI, (2005). doi: 10.1090/conm/385/07194.  Google Scholar

[4]

Ann. Inst. Henri Poincaré, Anal. Non. Lin., 26 (2009), 1453-1481. doi: 10.1016/j.anihpc.2009.01.001.  Google Scholar

[5]

J. Modern Dynamics, 4 (2010), 91-137. doi: 10.3934/jmd.2010.4.91.  Google Scholar

[6]

Communications in Mathematical Physics, 314 (2012), 689-773. doi: 10.1007/s00220-012-1538-4.  Google Scholar

[7]

Annales de L'Institut Fourier, 57 (2007), 127-154.  Google Scholar

[8]

in "Probabilistic and Geometric Structures in Dynamics" (eds. K. Burns, D. Dolgopyat and Ya. Pesin ), Contemp. Math., Amer. Math. Soc., 469 (2008), 29-68. doi: 10.1090/conm/469/09160.  Google Scholar

[9]

Nonlinearity, 15 (2002), 1905-1973. doi: 10.1088/0951-7715/15/6/309.  Google Scholar

[10]

Discrete Contin. Dyn. Syst., 33 (2013), 3355-3363. Google Scholar

[11]

, O. Butterey,, Private Communication., ().   Google Scholar

[12]

Ergodic Theory Dynam. Systems, 22 (2002), 1061-1078. doi: 10.1017/S0143385702000627.  Google Scholar

[13]

Trans. Amer. Math. Soc., 360 (2008), 4777-4814. doi: 10.1090/S0002-9947-08-04464-4.  Google Scholar

[14]

Ergodic Theory Dynam. Systems, 23 (2003), 175-191. doi: 10.1017/S0143385702000962.  Google Scholar

[15]

Ergodic Theory Dynam. Systems, 26 (2006), 189-218. doi: 10.1017/S0143385705000374.  Google Scholar

[16]

J. Diff. Geom., 79 (2008), 433-477.  Google Scholar

[17]

152 of Progress in Mathematics, Birkhäuser Boston Inc., Boston, MA, 1999. With Appendices by M. Katz, P. Pansu and S. Semmes.  Google Scholar

[18]

Probability Theory and Related Fields, 69 (1985), 461-478. doi: 10.1007/BF00532744.  Google Scholar

[19]

Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4), 28 (1999), 141-152.  Google Scholar

[20]

Dynamical Systems. Part II, 185-237, Pubbl. Cent. Ric. Mat. Ennio Giorgi, Scuola Norm. Sup., Pisa, (2003).  Google Scholar

[21]

Ergodic Theory and Dynamical Systems, 33 (2013), 168-182. doi: 10.1017/S0143385711000939.  Google Scholar

[22]

Ann. of Math. (2), 159 (2004), 1275-1312. doi: 10.4007/annals.2004.159.1275.  Google Scholar

[23]

Israel J. Math., 116 (2000), 223-248. doi: 10.1007/BF02773219.  Google Scholar

[24]

Studia Math., 76 (1983), 69-80.  Google Scholar

[25]

Discrete Contin. Dyn. Syst., 30 (2011), 917-944. doi: 10.3934/dcds.2011.30.917.  Google Scholar

[26]

Nonlinearity, 23 (2010), 1495-1545. doi: 10.1088/0951-7715/23/7/001.  Google Scholar

[27]

Calc. Var. Partial Differential Equations, 40 (2011), 99-124. doi: 10.1007/s00526-010-0335-1.  Google Scholar

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