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Weighted Green functions of nondegenerate polynomial skew products on $\mathbb{C}^2$
1. | Toba National College of Maritime Technology, Mie 517-8501, Japan |
References:
[1] |
E. Bedford and M. Jonsson, Dynamics of regular polynomial endomorphisms of $\mathbbC^k$, Amer. J. Math., 122 (2000), 153-212. |
[2] |
E. Bedford and J. Smillie, Polynomial diffeomorphisms of $\mathbbC^2$: Currents, equilibrium measure and hyperbolicity, Invent. Math., 103 (1991), 69-99.
doi: 10.1007/BF01239509. |
[3] |
L. DeMarco and S. L. Hruska, Axiom A polynomial skew products of $\mathbbC^2$ and their postcritical sets, Ergodic Theory Dynam. Systems, 28 (2008), 1749-1779.
doi: 10.1017/S0143385708000047. |
[4] |
T.-C. Dinh and N. Sibony, Dynamique des applications polynomiales semi-régulières, (French) [Dynamics of semiregular polynomial maps], Ark. Mat., 42 (2004), 61-85. |
[5] |
T.-C. Dinh, R. Dujardin and N. Sibony, On the dynamics near infinity of some polynomial mappings in $\mathbbC^2$, Math. Ann., 333 (2005), 703-739.
doi: 10.1007/s00208-005-0661-3. |
[6] |
C. Favre and V. Guedj, Dynamique des applications rationnelles des espaces multiprojectifs, (French) [Dynamics of rational mappings of multiprojective spaces], Indiana Univ. Math. J., 50 (2001), 881-934.
doi: 10.1512/iumj.2001.50.1880. |
[7] |
C. Favre and M. Jonsson, Eigenvaluations, Ann. Sci. École Norm. Sup., 40 (2007), 309-349. |
[8] |
C. Favre and M. Jonsson, Dynamical compactifications of $\mathbbC^2$, Ann. of Math., 173 (2011), 211-248.
doi: 10.4007/annals.2011.173.1.6. |
[9] |
V. Guedj, Dynamics of polynomial mappings of $\mathbbC^2$, Amer. J. Math., 124 (2002), 75-106.
doi: 10.1353/ajm.2002.0002. |
[10] |
V. Guedj, Dynamics of quadratic polynomial mappings of $\mathbbC^2$, Michigan Math. J., 52 (2004), 627-648.
doi: 10.1307/mmj/1100623417. |
[11] |
S.-M. Heinemann, Julia sets for holomorphic endomorphisms of $\mathbbC^n$, Ergodic Theory Dynam. Systems, 16 (1996), 1275-1296.
doi: 10.1017/S0143385700010026. |
[12] |
S.-M. Heinemann, Julia sets of skew products in $\mathbbC^2$, Kyushu J. Math., 52 (1998), 299-329.
doi: 10.2206/kyushujm.52.299. |
[13] |
M. Jonsson, Dynamics of polynomial skew products on $\mathbbC^2$, Math. Ann., 314 (1999), 403-447.
doi: 10.1007/s002080050301. |
[14] |
T. Ueda, Fatou sets in complex dynamics on projective spaces, J. Math. Soc. Japan, 46 (1994), 545-555.
doi: 10.2969/jmsj/04630545. |
[15] |
K. Ueno, Symmetries of Julia sets of nondegenerate polynomial skew products on $\mathbbC^2$, Michigan Math. J., 59 (2010), 153-168.
doi: 10.1307/mmj/1272376030. |
[16] |
G. Vigny, Dynamics semi-conjugated to a subshift for some polynomial mappings in $\mathbbC^2$, Publ. Mat., 51 (2007), 201-222. |
show all references
References:
[1] |
E. Bedford and M. Jonsson, Dynamics of regular polynomial endomorphisms of $\mathbbC^k$, Amer. J. Math., 122 (2000), 153-212. |
[2] |
E. Bedford and J. Smillie, Polynomial diffeomorphisms of $\mathbbC^2$: Currents, equilibrium measure and hyperbolicity, Invent. Math., 103 (1991), 69-99.
doi: 10.1007/BF01239509. |
[3] |
L. DeMarco and S. L. Hruska, Axiom A polynomial skew products of $\mathbbC^2$ and their postcritical sets, Ergodic Theory Dynam. Systems, 28 (2008), 1749-1779.
doi: 10.1017/S0143385708000047. |
[4] |
T.-C. Dinh and N. Sibony, Dynamique des applications polynomiales semi-régulières, (French) [Dynamics of semiregular polynomial maps], Ark. Mat., 42 (2004), 61-85. |
[5] |
T.-C. Dinh, R. Dujardin and N. Sibony, On the dynamics near infinity of some polynomial mappings in $\mathbbC^2$, Math. Ann., 333 (2005), 703-739.
doi: 10.1007/s00208-005-0661-3. |
[6] |
C. Favre and V. Guedj, Dynamique des applications rationnelles des espaces multiprojectifs, (French) [Dynamics of rational mappings of multiprojective spaces], Indiana Univ. Math. J., 50 (2001), 881-934.
doi: 10.1512/iumj.2001.50.1880. |
[7] |
C. Favre and M. Jonsson, Eigenvaluations, Ann. Sci. École Norm. Sup., 40 (2007), 309-349. |
[8] |
C. Favre and M. Jonsson, Dynamical compactifications of $\mathbbC^2$, Ann. of Math., 173 (2011), 211-248.
doi: 10.4007/annals.2011.173.1.6. |
[9] |
V. Guedj, Dynamics of polynomial mappings of $\mathbbC^2$, Amer. J. Math., 124 (2002), 75-106.
doi: 10.1353/ajm.2002.0002. |
[10] |
V. Guedj, Dynamics of quadratic polynomial mappings of $\mathbbC^2$, Michigan Math. J., 52 (2004), 627-648.
doi: 10.1307/mmj/1100623417. |
[11] |
S.-M. Heinemann, Julia sets for holomorphic endomorphisms of $\mathbbC^n$, Ergodic Theory Dynam. Systems, 16 (1996), 1275-1296.
doi: 10.1017/S0143385700010026. |
[12] |
S.-M. Heinemann, Julia sets of skew products in $\mathbbC^2$, Kyushu J. Math., 52 (1998), 299-329.
doi: 10.2206/kyushujm.52.299. |
[13] |
M. Jonsson, Dynamics of polynomial skew products on $\mathbbC^2$, Math. Ann., 314 (1999), 403-447.
doi: 10.1007/s002080050301. |
[14] |
T. Ueda, Fatou sets in complex dynamics on projective spaces, J. Math. Soc. Japan, 46 (1994), 545-555.
doi: 10.2969/jmsj/04630545. |
[15] |
K. Ueno, Symmetries of Julia sets of nondegenerate polynomial skew products on $\mathbbC^2$, Michigan Math. J., 59 (2010), 153-168.
doi: 10.1307/mmj/1272376030. |
[16] |
G. Vigny, Dynamics semi-conjugated to a subshift for some polynomial mappings in $\mathbbC^2$, Publ. Mat., 51 (2007), 201-222. |
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