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Energy identity for a class of approximate biharmonic maps into sphere in dimension four
A note on a sifting-type lemma
1. | School of Mathematics and Systems Science, Beihang University, Beijing 100191, China |
2. | Department of Mathematics, Nanjing University, Nanjing, 210093 |
References:
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J. Alves and V. Araújo, Hyperbolic times: frequency versus integrability, Ergod. Th. & Dynam. Sys., 24 (2004), 329-346.
doi: 10.1017/S0143385703000555. |
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S. Crovisier, Partial hyperbolicity far from homoclinic bifurcations, Advances in Mathematics, 226 (2011), 673-726.
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S. Gan, A generalized shadowing lemma, Discrete Cont. Dynam. Syst., 8 (2002), 627-632. |
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S. Gan and L. Wen, Nonsingular star flows satisfy axiom A and the no-cycle condition, Invent. Math., 164 (2006), 279-315.
doi: 10.1007/s00222-005-0479-3. |
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S. Liao, An existence theorem for periodic orbits, (Chinese) Beijing Daxue Xuebao, 1 (1979), 1-20. |
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R. Potrie and M. Sambarino, Codimension one generic homoclinic classes with interior, Bull. Braz. Math. Soc., 41 (2010), 125-138.doi: 10.1007/s00574-010-0006-z
doi: 10.1007/s00574-010-0006-z. |
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L. Wen, Generic diffeomorphisms away from homoclinic tangencies and heterodimensional cycles, Bull. Braz. Math. Soc., 35 (2004), 419-452. |
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L. Wen, The selecting lemma of Liao, Discrete Cont. Dynam. Syst., 20 (2008), 159-175.
doi: 10.3934/dcds.2008.20.159. |
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X. Wen, S. Gan and L. Wen, $C^1$-stably shadowable chain components are hyperbolic, J. Differential Equations, 246 (2009), 340-357.
doi: 10.1016/j.jde.2008.03.032. |
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P. Zhang, A diffeomorphism with global dominated splitting can not be minimal, Proc. Amer. Math. Soc., 140 (2012), 589-593. |
show all references
References:
[1] |
J. Alves and V. Araújo, Hyperbolic times: frequency versus integrability, Ergod. Th. & Dynam. Sys., 24 (2004), 329-346.
doi: 10.1017/S0143385703000555. |
[2] |
S. Crovisier, Partial hyperbolicity far from homoclinic bifurcations, Advances in Mathematics, 226 (2011), 673-726.
doi: 10.1016/j.aim.2010.07.013. |
[3] |
S. Gan, A generalized shadowing lemma, Discrete Cont. Dynam. Syst., 8 (2002), 627-632. |
[4] |
S. Gan and L. Wen, Nonsingular star flows satisfy axiom A and the no-cycle condition, Invent. Math., 164 (2006), 279-315.
doi: 10.1007/s00222-005-0479-3. |
[5] |
S. Liao, An existence theorem for periodic orbits, (Chinese) Beijing Daxue Xuebao, 1 (1979), 1-20. |
[6] |
S. Liao, On the stability conjecture, Chinese Annals of Math., 1 (1980), 9-30. |
[7] |
V. Pliss, On a conjecture of Smale, Diff. Uravnenija, 8 (1972), 268-282. |
[8] |
R. Potrie and M. Sambarino, Codimension one generic homoclinic classes with interior, Bull. Braz. Math. Soc., 41 (2010), 125-138.doi: 10.1007/s00574-010-0006-z
doi: 10.1007/s00574-010-0006-z. |
[9] |
L. Wen, Generic diffeomorphisms away from homoclinic tangencies and heterodimensional cycles, Bull. Braz. Math. Soc., 35 (2004), 419-452. |
[10] |
L. Wen, The selecting lemma of Liao, Discrete Cont. Dynam. Syst., 20 (2008), 159-175.
doi: 10.3934/dcds.2008.20.159. |
[11] |
X. Wen, S. Gan and L. Wen, $C^1$-stably shadowable chain components are hyperbolic, J. Differential Equations, 246 (2009), 340-357.
doi: 10.1016/j.jde.2008.03.032. |
[12] |
P. Zhang, A diffeomorphism with global dominated splitting can not be minimal, Proc. Amer. Math. Soc., 140 (2012), 589-593. |
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