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Dynamical Borel–Cantelli lemmas
Lund University, Sweden |
This paper is a study of Borel–Cantelli lemmas in dynamical systems. D. Kleinbock and G. Margulis [
References:
[1] |
E. Borel,
Les probabilit$\acute{e}$s d$\acute{e}$nombrables et leurs applications arithmetiques, Rend. Circ. Mat. Palermo, 27 (1909), 247-271.
doi: 10.1007/BF03019651. |
[2] |
F. P. Cantelli,
Sulla probabilit$\grave{a}$ come limite della frequenza, Atti delta Reale Accademia Nationale dei Lincei, Serie V, Rendicotti, 26 (1917), 39-45.
|
[3] |
N. Chernov and D. Kleinbock,
Dynamical Borel–Cantelli lemmas for Gibbs measures, Isreal J. Math., 122 (2001), 1-27.
doi: 10.1007/BF02809888. |
[4] |
C. Gupta, M. Nicol and W. Ott,
A Borel–Cantelli lemma for non–uniformly expanding dynamical systems, Nonlinearity, 23 (2010), 1991-2008.
doi: 10.1088/0951-7715/23/8/010. |
[5] |
N. Haydn, M. Nicol, T. Persson and S. Vaienti,
A note on Borel–Cantelli lemmas for non–uniformly hyperbolic dynamical systems, Ergod. Th. & Dynam. Sys., 33 (2013), 475-498.
doi: 10.1017/S014338571100099X. |
[6] |
D. Khoshnevisan, Probability, Graduate Studies in Mathematics, 80, AMS, 2007.
doi: 10.1090/gsm/080. |
[7] |
D. Kleinbock and G. Margulis,
Logarithm laws for flows on homogeneous spaces, Inv. Math., 138 (1999), 451-494.
doi: 10.1007/s002220050350. |
[8] |
W. J. LeVeque,
On the frequency of small fractional parts in certain real sequences III, Journal Reine Angew. Math., 202 (1959), 215-220.
doi: 10.1515/crll.1959.202.215. |
[9] |
W. Philipp,
Some metrical theorems in number theory, Pacific J. Math, 20 (1967), 109-127.
doi: 10.2140/pjm.1967.20.109. |
[10] |
W. M. Schmidt,
A metrical theorem in of Diophantine approximation, Canad. J. Math, 12 (1960), 619-631.
doi: 10.4153/CJM-1960-056-0. |
[11] |
W. M. Schmidt,
Metrical theorems on fractional parts of sequences, Transactions AMS, 110 (1964), 493-518.
doi: 10.1090/S0002-9947-1964-0159802-4. |
[12] |
C. E. Silva, Invitation to Ergodic Theory, American Mathematical Soc., 2008.
doi: 10.1090/stml/042. |
[13] |
V.Sprindžuk, Metric Theory of Diophantine Approximations, J. Wiley & Sons, New York–Toronto–London, 1979. |
show all references
References:
[1] |
E. Borel,
Les probabilit$\acute{e}$s d$\acute{e}$nombrables et leurs applications arithmetiques, Rend. Circ. Mat. Palermo, 27 (1909), 247-271.
doi: 10.1007/BF03019651. |
[2] |
F. P. Cantelli,
Sulla probabilit$\grave{a}$ come limite della frequenza, Atti delta Reale Accademia Nationale dei Lincei, Serie V, Rendicotti, 26 (1917), 39-45.
|
[3] |
N. Chernov and D. Kleinbock,
Dynamical Borel–Cantelli lemmas for Gibbs measures, Isreal J. Math., 122 (2001), 1-27.
doi: 10.1007/BF02809888. |
[4] |
C. Gupta, M. Nicol and W. Ott,
A Borel–Cantelli lemma for non–uniformly expanding dynamical systems, Nonlinearity, 23 (2010), 1991-2008.
doi: 10.1088/0951-7715/23/8/010. |
[5] |
N. Haydn, M. Nicol, T. Persson and S. Vaienti,
A note on Borel–Cantelli lemmas for non–uniformly hyperbolic dynamical systems, Ergod. Th. & Dynam. Sys., 33 (2013), 475-498.
doi: 10.1017/S014338571100099X. |
[6] |
D. Khoshnevisan, Probability, Graduate Studies in Mathematics, 80, AMS, 2007.
doi: 10.1090/gsm/080. |
[7] |
D. Kleinbock and G. Margulis,
Logarithm laws for flows on homogeneous spaces, Inv. Math., 138 (1999), 451-494.
doi: 10.1007/s002220050350. |
[8] |
W. J. LeVeque,
On the frequency of small fractional parts in certain real sequences III, Journal Reine Angew. Math., 202 (1959), 215-220.
doi: 10.1515/crll.1959.202.215. |
[9] |
W. Philipp,
Some metrical theorems in number theory, Pacific J. Math, 20 (1967), 109-127.
doi: 10.2140/pjm.1967.20.109. |
[10] |
W. M. Schmidt,
A metrical theorem in of Diophantine approximation, Canad. J. Math, 12 (1960), 619-631.
doi: 10.4153/CJM-1960-056-0. |
[11] |
W. M. Schmidt,
Metrical theorems on fractional parts of sequences, Transactions AMS, 110 (1964), 493-518.
doi: 10.1090/S0002-9947-1964-0159802-4. |
[12] |
C. E. Silva, Invitation to Ergodic Theory, American Mathematical Soc., 2008.
doi: 10.1090/stml/042. |
[13] |
V.Sprindžuk, Metric Theory of Diophantine Approximations, J. Wiley & Sons, New York–Toronto–London, 1979. |
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