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On the Allen-Cahn equation in the Grushin plane: A monotone entire solution that is not one-dimensional
Maximal abelian torsion subgroups of Diff( C,0)
1. | Ramakrishna Mission Vivekananda University, Belur Math, WB-711202 |
References:
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I. N. Baker, Fractional iteration near a fixed point of multiplier 1, J. Austral. Math. Soc, 4 (1964), 143-148.
doi: 10.1017/S144678870002334X. |
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A. D. Brjuno, Analytical form of differential equations, Transactions Moscow Math. Soc., 25 (1971), 131-288. |
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J. Ecalle, Théorie itérative: introduction à la théorie des invariantes holomorphes, J. Math pures et appliqués, 54 (1975), 183-258. |
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J. Moser, On commuting circle mappings and simultaneous Diophantine approximations, Math. Zeitschrift, 205 (1990), 105-121.
doi: 10.1007/BF02571227. |
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R. Perez-Marco, Solution complète au problème de Siegel de linéarisation d'une application holomorphe au voisinage d'un point fixe (d'après J.C.Yoccoz), Seminar Bourbaki, 34 Exp. No. 753. |
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R. Perez-Marco, Uncountable number of symmetries for non-linearisable holomorphic dynamics, Inventiones Mathematicae, 119 (1995), 67-127.
doi: 10.1007/BF01245175. |
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S. M. Voronin, Analytic classification of germs of conformal mappings (C,0) $\to$ (C,0) with identity linear part, Funktsional Anal. i Prilozhen, 16 (1982), 1-17. |
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J. C. Yoccoz, Petits diviseurs en dimension 1, Asterisque, 231 (1995), 3-88. |
show all references
References:
[1] |
I. N. Baker, Fractional iteration near a fixed point of multiplier 1, J. Austral. Math. Soc, 4 (1964), 143-148.
doi: 10.1017/S144678870002334X. |
[2] |
A. D. Brjuno, Analytical form of differential equations, Transactions Moscow Math. Soc., 25 (1971), 131-288. |
[3] |
J. Ecalle, Théorie itérative: introduction à la théorie des invariantes holomorphes, J. Math pures et appliqués, 54 (1975), 183-258. |
[4] |
J. Moser, On commuting circle mappings and simultaneous Diophantine approximations, Math. Zeitschrift, 205 (1990), 105-121.
doi: 10.1007/BF02571227. |
[5] |
R. Perez-Marco, Solution complète au problème de Siegel de linéarisation d'une application holomorphe au voisinage d'un point fixe (d'après J.C.Yoccoz), Seminar Bourbaki, 34 Exp. No. 753. |
[6] |
R. Perez-Marco, Uncountable number of symmetries for non-linearisable holomorphic dynamics, Inventiones Mathematicae, 119 (1995), 67-127.
doi: 10.1007/BF01245175. |
[7] |
S. M. Voronin, Analytic classification of germs of conformal mappings (C,0) $\to$ (C,0) with identity linear part, Funktsional Anal. i Prilozhen, 16 (1982), 1-17. |
[8] |
J. C. Yoccoz, Petits diviseurs en dimension 1, Asterisque, 231 (1995), 3-88. |
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