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The Cauchy problem for a tenth-order thin film equation II. Oscillatory source-type and fundamental similarity solutions
On special flows over IETs that are not isomorphic to their inverses
1. | Faculty of Mathematics and Computer Science, Nicolaus Copernicus University, ul. Chopina 12/18, 87-100 Toruń, Poland |
References:
[1] |
H. Anzai, On an example of a measure preserving transformation which is not conjugate to its inverse,, Proc. Japan Acad., 27 (1951), 517.
doi: 10.3792/pja/1195571227. |
[2] |
I. P. Cornfeld, S. V. Fomin and Ya. G. Sinai, Ergodic Theory,, Springer-Verlag, (1982).
doi: 10.1007/978-1-4615-6927-5. |
[3] |
A. I. Danilenko and V. V. Ryzhikov, On self-similarities of ergodic flows,, Proc. Lond. Math. Soc., 104 (2012), 431.
doi: 10.1112/plms/pdr032. |
[4] |
A. del Junco, Disjointness of measure-preserving transformations, minimal self-joinings and category,, in Ergodic theory and dynamical systems, 10 (1981), 1979.
doi: 10.1007/978-1-4899-6696-4_3. |
[5] |
K. Frączek, Density of mild mixing property for vertical flows of Abelian differentials,, Proc. Amer. Math. Soc., 137 (2009), 4129.
doi: 10.1090/S0002-9939-09-10025-4. |
[6] |
K. Frączek, J. Kułaga and M. Lemańczyk, Non-reversibility and self-joinings of higher orders for ergodic flows,, J. Anal. Math., 122 (2014), 163.
doi: 10.1007/s11854-014-0007-8. |
[7] |
K. Frączek and M. Lemańczyk, On the self-similarity problem for ergodic flows,, Proc. Lond. Math. Soc., 99 (2009), 658.
doi: 10.1112/plms/pdp013. |
[8] |
K. Frączek and M. Lemańczyk, A class of special flows over irrational rotations which is disjoint from mixing flows,, Ergodic Theory Dynam. Systems, 24 (2004), 1083.
doi: 10.1017/S0143385704000112. |
[9] |
K. Frączek and M. Lemańczyk, On disjointness properties of some smooth flows,, Fund. Math., 185 (2005), 117.
doi: 10.4064/fm185-2-2. |
[10] |
E. Glasner, Ergodic Theory Via Joinings,, Mathematical Surveys and Monographs, (2003).
doi: 10.1090/surv/101. |
[11] |
P. R. Halmos and J. von Neumann, Operator methods in classical mechanics. II,, Ann. of Math. (2), 43 (1942), 332.
doi: 10.2307/1968872. |
[12] |
A. Katok, Interval exchange transformations and some special flows are not mixing,, Israel J. Math., 35 (1980), 301.
doi: 10.1007/BF02760655. |
[13] |
M. Keane, Interval exchange transformations,, Math. Z., 141 (1975), 25.
doi: 10.1007/BF01236981. |
[14] |
J. King, Joining-rank and the structure of finite rank mixing transformations,, J. Anal. Math., 51 (1988), 182.
doi: 10.1007/BF02791123. |
[15] |
J. Kułaga, On the self-similarity problem for smooth flows on orientable surfaces,, Ergodic Theory Dynam. Systems, 32 (2012), 1615.
doi: 10.1017/S0143385711000459. |
[16] |
G. Rauzy, Échanges d'intervalles et transformations induites,, Acta Arith., 34 (1979), 315.
|
[17] |
V. V. Ryzhikov, Partial multiple mixing on subsequences can distinguish between automorphisms $T$ and $T^{-1}$,, Math. Notes, 74 (2003), 841.
doi: 10.1023/B:MATN.0000009020.82284.54. |
[18] |
W. Veech, Interval exchange transformations,, J. Anal. Math., 33 (1978), 222.
doi: 10.1007/BF02790174. |
[19] |
W. Veech, Projective Swiss cheeses and uniquely ergodic interval exchange transformations,, Ergodic theory and dynamical systems, 10 (1981), 1979.
doi: 10.1007/978-1-4899-6696-4_5. |
[20] |
W. Veech, Gauss measures for transformations on the space of interval exchange maps,, Ann. of Math. (2), 115 (1982), 201.
doi: 10.2307/1971391. |
[21] |
W. Veech, The metric theory of interval exchange transformations. I. Generic spectral properties,, Amer. J. Math., 106 (1984), 1331.
doi: 10.2307/2374396. |
[22] |
M. Viana, Ergodic theory of interval exchange maps,, Rev. Mat. Complut., 19 (2006), 7.
|
show all references
References:
[1] |
H. Anzai, On an example of a measure preserving transformation which is not conjugate to its inverse,, Proc. Japan Acad., 27 (1951), 517.
doi: 10.3792/pja/1195571227. |
[2] |
I. P. Cornfeld, S. V. Fomin and Ya. G. Sinai, Ergodic Theory,, Springer-Verlag, (1982).
doi: 10.1007/978-1-4615-6927-5. |
[3] |
A. I. Danilenko and V. V. Ryzhikov, On self-similarities of ergodic flows,, Proc. Lond. Math. Soc., 104 (2012), 431.
doi: 10.1112/plms/pdr032. |
[4] |
A. del Junco, Disjointness of measure-preserving transformations, minimal self-joinings and category,, in Ergodic theory and dynamical systems, 10 (1981), 1979.
doi: 10.1007/978-1-4899-6696-4_3. |
[5] |
K. Frączek, Density of mild mixing property for vertical flows of Abelian differentials,, Proc. Amer. Math. Soc., 137 (2009), 4129.
doi: 10.1090/S0002-9939-09-10025-4. |
[6] |
K. Frączek, J. Kułaga and M. Lemańczyk, Non-reversibility and self-joinings of higher orders for ergodic flows,, J. Anal. Math., 122 (2014), 163.
doi: 10.1007/s11854-014-0007-8. |
[7] |
K. Frączek and M. Lemańczyk, On the self-similarity problem for ergodic flows,, Proc. Lond. Math. Soc., 99 (2009), 658.
doi: 10.1112/plms/pdp013. |
[8] |
K. Frączek and M. Lemańczyk, A class of special flows over irrational rotations which is disjoint from mixing flows,, Ergodic Theory Dynam. Systems, 24 (2004), 1083.
doi: 10.1017/S0143385704000112. |
[9] |
K. Frączek and M. Lemańczyk, On disjointness properties of some smooth flows,, Fund. Math., 185 (2005), 117.
doi: 10.4064/fm185-2-2. |
[10] |
E. Glasner, Ergodic Theory Via Joinings,, Mathematical Surveys and Monographs, (2003).
doi: 10.1090/surv/101. |
[11] |
P. R. Halmos and J. von Neumann, Operator methods in classical mechanics. II,, Ann. of Math. (2), 43 (1942), 332.
doi: 10.2307/1968872. |
[12] |
A. Katok, Interval exchange transformations and some special flows are not mixing,, Israel J. Math., 35 (1980), 301.
doi: 10.1007/BF02760655. |
[13] |
M. Keane, Interval exchange transformations,, Math. Z., 141 (1975), 25.
doi: 10.1007/BF01236981. |
[14] |
J. King, Joining-rank and the structure of finite rank mixing transformations,, J. Anal. Math., 51 (1988), 182.
doi: 10.1007/BF02791123. |
[15] |
J. Kułaga, On the self-similarity problem for smooth flows on orientable surfaces,, Ergodic Theory Dynam. Systems, 32 (2012), 1615.
doi: 10.1017/S0143385711000459. |
[16] |
G. Rauzy, Échanges d'intervalles et transformations induites,, Acta Arith., 34 (1979), 315.
|
[17] |
V. V. Ryzhikov, Partial multiple mixing on subsequences can distinguish between automorphisms $T$ and $T^{-1}$,, Math. Notes, 74 (2003), 841.
doi: 10.1023/B:MATN.0000009020.82284.54. |
[18] |
W. Veech, Interval exchange transformations,, J. Anal. Math., 33 (1978), 222.
doi: 10.1007/BF02790174. |
[19] |
W. Veech, Projective Swiss cheeses and uniquely ergodic interval exchange transformations,, Ergodic theory and dynamical systems, 10 (1981), 1979.
doi: 10.1007/978-1-4899-6696-4_5. |
[20] |
W. Veech, Gauss measures for transformations on the space of interval exchange maps,, Ann. of Math. (2), 115 (1982), 201.
doi: 10.2307/1971391. |
[21] |
W. Veech, The metric theory of interval exchange transformations. I. Generic spectral properties,, Amer. J. Math., 106 (1984), 1331.
doi: 10.2307/2374396. |
[22] |
M. Viana, Ergodic theory of interval exchange maps,, Rev. Mat. Complut., 19 (2006), 7.
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