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On the mixing properties of piecewise expanding maps under composition with permutations
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An alternative approach to generalised BV and the application to expanding interval maps
1. | Dipartimento di Matematica, II Università di Roma (Tor Vergata), Via della Ricerca Scientica, 00133 Roma, Italy |
References:
[1] |
V. Baladi, "Positive Transfer Operators & Decay of Correlation," 16 of Advanced Series in Nonlinear Dynamics, World Scientific, Singapore, 2000.
doi: 10.1142/9789812813633. |
[2] |
J. Bergh and J. Löfström, "Interpolation Spaces, An Introduction," 223, Grundlehren der Mathematischen Wissenschaften. Springer-Verlag, 1976. |
[3] |
H. Hennion, Sur un théorème spectral et son application aux noyaux lipchitziens, Proc. Amer. Math. Soc., 118 (1993), 627-634.
doi: 10.2307/2160348. |
[4] |
G. Keller, Generalized bounded variation and applications to piecewise monotonic transformations, Z. Wahrsch. Verw. Gebiete, 69 (1985), 461-478.
doi: 10.1007/BF00532744. |
[5] |
S. Luzzatto, I. Melbourne and F. Paccaut, The Lorenz attractor is mixing, Comm. Math. Phys., 260 (2005), 393-401.
doi: 10.1007/s00220-005-1411-9. |
[6] |
R. D. Nussbaum, The radius of the essential spectrum, Duke Math. J., 37 (1970), 473-478. |
[7] |
M. Pollicott, On the rate of mixing of Axiom A flows, Invent. Math., 81 (1985), 413-426.
doi: 10.1007/BF01388579. |
[8] |
D. Thomine, A spectral gap for transfer operators of piecewise expanding maps, Discrete Contin. Dyn. Syst., 30 (2011), 917-944.
doi: 10.3934/dcds.2011.30.917. |
show all references
References:
[1] |
V. Baladi, "Positive Transfer Operators & Decay of Correlation," 16 of Advanced Series in Nonlinear Dynamics, World Scientific, Singapore, 2000.
doi: 10.1142/9789812813633. |
[2] |
J. Bergh and J. Löfström, "Interpolation Spaces, An Introduction," 223, Grundlehren der Mathematischen Wissenschaften. Springer-Verlag, 1976. |
[3] |
H. Hennion, Sur un théorème spectral et son application aux noyaux lipchitziens, Proc. Amer. Math. Soc., 118 (1993), 627-634.
doi: 10.2307/2160348. |
[4] |
G. Keller, Generalized bounded variation and applications to piecewise monotonic transformations, Z. Wahrsch. Verw. Gebiete, 69 (1985), 461-478.
doi: 10.1007/BF00532744. |
[5] |
S. Luzzatto, I. Melbourne and F. Paccaut, The Lorenz attractor is mixing, Comm. Math. Phys., 260 (2005), 393-401.
doi: 10.1007/s00220-005-1411-9. |
[6] |
R. D. Nussbaum, The radius of the essential spectrum, Duke Math. J., 37 (1970), 473-478. |
[7] |
M. Pollicott, On the rate of mixing of Axiom A flows, Invent. Math., 81 (1985), 413-426.
doi: 10.1007/BF01388579. |
[8] |
D. Thomine, A spectral gap for transfer operators of piecewise expanding maps, Discrete Contin. Dyn. Syst., 30 (2011), 917-944.
doi: 10.3934/dcds.2011.30.917. |
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