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Dynamics of continued fractions and kneading sequences of unimodal maps
1. | Dipartimento di Matematica, Università di Pisa, Largo Bruno Pontecorvo 5, I-56127, Italy, Italy |
2. | Dipartimento di Matematica e Informatica, Università di Camerino, via Madonna delle Carceri, I-62032 Camerino |
3. | Department of Mathematics, Harvard University, One Oxford Street Cambridge, MA 02138, United States |
References:
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Acta Math., 195 (2005), 1-20.
doi: 10.1007/BF02588048. |
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Thèse d'État, Université Bordeaux I, 1983. Google Scholar |
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C. R. Acad. Sci. Paris Sér. I, Math., 296 (1983), 159-162. |
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Acta Math. Hungar., 91 (2001), 325-332.
doi: 10.1023/A:1010667918943. |
[5] |
Amer. Math. Monthly, 107 (2000), 448-449. |
[6] |
Coll. Math., 116 (2009), 165-189. |
[7] |
Ergodic Theory Dynam. Systems, 32 (2012), 1249-1269.
doi: 10.1017/S0143385711000447. |
[8] |
Nonlinearity, 23 (2010), 2429-2456.
doi: 10.1088/0951-7715/23/10/005. |
[9] |
Theoret. Comput. Sci., 218 (1999), 3-12. |
[10] |
Springer-Verlag, Berlin, Heidelberg, 1993. |
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Acta Math. Hungar, 119, (2008), 57-62.
doi: 10.1007/s10474-007-6252-x. |
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in "Real and Complex Dynamical Systems (Hillerød, 1993)'', NATO Adv. Sci. Inst. Ser. C, Math. Phys. Sci., 464, Kluwer, Dordrecht (1995), 65-87. |
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Acta Math. Hungar, 58 (1991), 129-132.
doi: 10.1109/LICS.1991.151636. |
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Bull. Soc. Math. France, 118 (1990), 377-390. |
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$2^{nd}$ edition, John Wiley and Sons, Chichester UK, 2003. |
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Ann. of Math., 146 (1997), 1-52. |
[17] |
J. Number Theory, 40 (1992), 336-358.
doi: 10.1016/0022-314X(92)90006-B. |
[18] |
Far East J. Dyn. Syst., 6 (2004), 79-96. |
[19] |
J. Stat. Phys., 61 (1990), 263-291.
doi: 10.1007/BF01013965. |
[20] |
Amer. Math. Monthly, 105 (1998), 936-939. |
[21] |
J. Number Theory, 122 (2007), 157-183. |
[22] |
Nonlinearity, 25 (2012), 2207-2243.
doi: 10.1088/0951-7715/25/8/2207. |
[23] |
Discrete Contin. Dyn. Syst., 20 (2008), 673-711. |
[24] |
Acta Math., 178 (1997), 185-247, 247-297.
doi: 10.1007/BF02392694. |
[25] |
Math. Annalen, 101 (1929), 342-366. Corrigendum, 103 (1930), 532. |
[26] |
Ark. Mat., 25 (1987), 41-89.
doi: 10.1007/BF02384436. |
[27] |
in "Dynamical Systems (College Park, MD, 1986-87)'', Lecture Notes in Math., 1342, Springer, Berlin (1988), 465-563. |
[28] |
C. G. Moreira, Geometric properties of the Markov and Lagrange spectra,, available from: , (). Google Scholar |
[29] |
Tokyo J. Math., 4 (1981), 399-426.
doi: 10.3836/tjm/1270215165. |
[30] |
Nonlinearity, 21 (2008), 1207-1225.
doi: 10.1088/0951-7715/21/6/003. |
[31] |
Trans. Amer. Math. Soc., 53 (1943), 427-439. |
[32] |
in "Complex Dynamics: Families and Friends'' (eds. D. Schleicher and N. Selinger), A K Peters, Wellesley, MA, (2009), 3-137.
doi: 10.1016/j.phycom.2009.02.007. |
[33] |
G. Tiozzo, The entropy of Nakada's $\alpha$-continued fractions: analytical results,, to appear on Ann. Sc. Norm. Super. Pisa Cl. Sci., (). Google Scholar |
[34] |
Ergodic Theory Dynam. Systems, 23 (2003), 637-660. |
show all references
References:
[1] |
Acta Math., 195 (2005), 1-20.
doi: 10.1007/BF02588048. |
[2] |
Thèse d'État, Université Bordeaux I, 1983. Google Scholar |
[3] |
C. R. Acad. Sci. Paris Sér. I, Math., 296 (1983), 159-162. |
[4] |
Acta Math. Hungar., 91 (2001), 325-332.
doi: 10.1023/A:1010667918943. |
[5] |
Amer. Math. Monthly, 107 (2000), 448-449. |
[6] |
Coll. Math., 116 (2009), 165-189. |
[7] |
Ergodic Theory Dynam. Systems, 32 (2012), 1249-1269.
doi: 10.1017/S0143385711000447. |
[8] |
Nonlinearity, 23 (2010), 2429-2456.
doi: 10.1088/0951-7715/23/10/005. |
[9] |
Theoret. Comput. Sci., 218 (1999), 3-12. |
[10] |
Springer-Verlag, Berlin, Heidelberg, 1993. |
[11] |
Acta Math. Hungar, 119, (2008), 57-62.
doi: 10.1007/s10474-007-6252-x. |
[12] |
in "Real and Complex Dynamical Systems (Hillerød, 1993)'', NATO Adv. Sci. Inst. Ser. C, Math. Phys. Sci., 464, Kluwer, Dordrecht (1995), 65-87. |
[13] |
Acta Math. Hungar, 58 (1991), 129-132.
doi: 10.1109/LICS.1991.151636. |
[14] |
Bull. Soc. Math. France, 118 (1990), 377-390. |
[15] |
$2^{nd}$ edition, John Wiley and Sons, Chichester UK, 2003. |
[16] |
Ann. of Math., 146 (1997), 1-52. |
[17] |
J. Number Theory, 40 (1992), 336-358.
doi: 10.1016/0022-314X(92)90006-B. |
[18] |
Far East J. Dyn. Syst., 6 (2004), 79-96. |
[19] |
J. Stat. Phys., 61 (1990), 263-291.
doi: 10.1007/BF01013965. |
[20] |
Amer. Math. Monthly, 105 (1998), 936-939. |
[21] |
J. Number Theory, 122 (2007), 157-183. |
[22] |
Nonlinearity, 25 (2012), 2207-2243.
doi: 10.1088/0951-7715/25/8/2207. |
[23] |
Discrete Contin. Dyn. Syst., 20 (2008), 673-711. |
[24] |
Acta Math., 178 (1997), 185-247, 247-297.
doi: 10.1007/BF02392694. |
[25] |
Math. Annalen, 101 (1929), 342-366. Corrigendum, 103 (1930), 532. |
[26] |
Ark. Mat., 25 (1987), 41-89.
doi: 10.1007/BF02384436. |
[27] |
in "Dynamical Systems (College Park, MD, 1986-87)'', Lecture Notes in Math., 1342, Springer, Berlin (1988), 465-563. |
[28] |
C. G. Moreira, Geometric properties of the Markov and Lagrange spectra,, available from: , (). Google Scholar |
[29] |
Tokyo J. Math., 4 (1981), 399-426.
doi: 10.3836/tjm/1270215165. |
[30] |
Nonlinearity, 21 (2008), 1207-1225.
doi: 10.1088/0951-7715/21/6/003. |
[31] |
Trans. Amer. Math. Soc., 53 (1943), 427-439. |
[32] |
in "Complex Dynamics: Families and Friends'' (eds. D. Schleicher and N. Selinger), A K Peters, Wellesley, MA, (2009), 3-137.
doi: 10.1016/j.phycom.2009.02.007. |
[33] |
G. Tiozzo, The entropy of Nakada's $\alpha$-continued fractions: analytical results,, to appear on Ann. Sc. Norm. Super. Pisa Cl. Sci., (). Google Scholar |
[34] |
Ergodic Theory Dynam. Systems, 23 (2003), 637-660. |
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