-
Previous Article
Almost every interval translation map of three intervals is finite type
- DCDS Home
- This Issue
-
Next Article
Scattering theory for the wave equation of a Hartree type in three space dimensions
Weighted Green functions of polynomial skew products on $\mathbb{C}^2$
1. | Toba National College of Maritime Technology, Mie 517-8501 |
References:
[1] |
E. Bedford and M. Jonsson, Dynamics of regular polynomial endomorphisms of $\mathbbC^k$, Amer. J. Math., 122 (2000), 153-212.
doi: 10.1353/ajm.2000.0001. |
[2] |
S. Boucksom, C. Favre and M. Jonsson, Degree growth of meromorphic surface maps, Duke Math. J., 141 (2008), 519-538.
doi: 10.1215/00127094-2007-004. |
[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] |
J. Diller and V. Guedj, Regularity of dynamical Green's functions, Trans. Amer. Math. Soc., 361 (2009), 4783-4805.
doi: 10.1090/S0002-9947-09-04740-0. |
[5] |
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. |
[6] |
C. Favre and M. Jonsson, The Valuative Tree, Lecture Notes in Mathematics, 1853. Springer-Verlag, Berlin, 2004.
doi: 10.1007/b100262. |
[7] |
C. Favre and M. Jonsson, Eigenvaluations, Ann. Sci. École Norm. Sup. (4), 40 (2007), 309-349.
doi: 10.1016/j.ansens.2007.01.002. |
[8] |
C. Favre and M. Jonsson, Dynamical compactifications of $\mathbbC^2$, Ann. of Math. (2), 173 (2011), 211-249.
doi: 10.4007/annals.2011.173.1.6. |
[9] |
J. E. Fornæss and N. Sibony, Complex Dynamics in Higher Dimension. II, Modern methods in complex analysis (Princeton, NJ, 1992), 135-182, Ann. of Math. Stud., 137, Princeton Univ. Press, Princeton, NJ, 1995. |
[10] |
V. Guedj, Dynamics of polynomial mappings of $\mathbbC^2$, Amer. J. Math., 124 (2002), 75-106.
doi: 10.1353/ajm.2002.0002. |
[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] |
S. L. Hruska and R. K. W. Roeder, Topology of Fatou components for endomorphisms of $\mathbb{CP}^k$: linking with the Green's current, Fund. Math., 210 (2010), 73-98.
doi: 10.4064/fm210-1-4. |
[14] |
M. Jonsson, Dynamics of polynomial skew products on $\mathbbC^2$, Math. Ann., 314 (1999), 403-447.
doi: 10.1007/s002080050301. |
[15] |
R. K. W. Roeder, A dichotomy for Fatou components of polynomial skew products, Conform. Geom. Dyn., 15 (2011), 7-19.
doi: 10.1090/S1088-4173-2011-00223-2. |
[16] |
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. |
[17] |
K. Ueno, Weighted Green functions of nondegenerate polynomial skew products on $\mathbbC^2$, Discrete Contin. Dyn. Syst., 31 (2011), 985-996.
doi: 10.3934/dcds.2011.31.985. |
[18] |
K. Ueno, Fiberwise Green functions of skew products semiconjugate to some polynomial products on $\mathbbC^2$, Kodai Math. J., 35 (2012), 345-357.
doi: 10.2996/kmj/1341401055. |
[19] |
K. Ueno, Polynomial skew products whose Julia sets have infinitely many symmetries,, submitted., ().
|
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.
doi: 10.1353/ajm.2000.0001. |
[2] |
S. Boucksom, C. Favre and M. Jonsson, Degree growth of meromorphic surface maps, Duke Math. J., 141 (2008), 519-538.
doi: 10.1215/00127094-2007-004. |
[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] |
J. Diller and V. Guedj, Regularity of dynamical Green's functions, Trans. Amer. Math. Soc., 361 (2009), 4783-4805.
doi: 10.1090/S0002-9947-09-04740-0. |
[5] |
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. |
[6] |
C. Favre and M. Jonsson, The Valuative Tree, Lecture Notes in Mathematics, 1853. Springer-Verlag, Berlin, 2004.
doi: 10.1007/b100262. |
[7] |
C. Favre and M. Jonsson, Eigenvaluations, Ann. Sci. École Norm. Sup. (4), 40 (2007), 309-349.
doi: 10.1016/j.ansens.2007.01.002. |
[8] |
C. Favre and M. Jonsson, Dynamical compactifications of $\mathbbC^2$, Ann. of Math. (2), 173 (2011), 211-249.
doi: 10.4007/annals.2011.173.1.6. |
[9] |
J. E. Fornæss and N. Sibony, Complex Dynamics in Higher Dimension. II, Modern methods in complex analysis (Princeton, NJ, 1992), 135-182, Ann. of Math. Stud., 137, Princeton Univ. Press, Princeton, NJ, 1995. |
[10] |
V. Guedj, Dynamics of polynomial mappings of $\mathbbC^2$, Amer. J. Math., 124 (2002), 75-106.
doi: 10.1353/ajm.2002.0002. |
[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] |
S. L. Hruska and R. K. W. Roeder, Topology of Fatou components for endomorphisms of $\mathbb{CP}^k$: linking with the Green's current, Fund. Math., 210 (2010), 73-98.
doi: 10.4064/fm210-1-4. |
[14] |
M. Jonsson, Dynamics of polynomial skew products on $\mathbbC^2$, Math. Ann., 314 (1999), 403-447.
doi: 10.1007/s002080050301. |
[15] |
R. K. W. Roeder, A dichotomy for Fatou components of polynomial skew products, Conform. Geom. Dyn., 15 (2011), 7-19.
doi: 10.1090/S1088-4173-2011-00223-2. |
[16] |
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. |
[17] |
K. Ueno, Weighted Green functions of nondegenerate polynomial skew products on $\mathbbC^2$, Discrete Contin. Dyn. Syst., 31 (2011), 985-996.
doi: 10.3934/dcds.2011.31.985. |
[18] |
K. Ueno, Fiberwise Green functions of skew products semiconjugate to some polynomial products on $\mathbbC^2$, Kodai Math. J., 35 (2012), 345-357.
doi: 10.2996/kmj/1341401055. |
[19] |
K. Ueno, Polynomial skew products whose Julia sets have infinitely many symmetries,, submitted., ().
|
[1] |
Peng Sun. Measures of intermediate entropies for skew product diffeomorphisms. Discrete and Continuous Dynamical Systems, 2010, 27 (3) : 1219-1231. doi: 10.3934/dcds.2010.27.1219 |
[2] |
Kohei Ueno. Weighted Green functions of nondegenerate polynomial skew products on $\mathbb{C}^2$. Discrete and Continuous Dynamical Systems, 2011, 31 (3) : 985-996. doi: 10.3934/dcds.2011.31.985 |
[3] |
Kyoungsun Kim, Gen Nakamura, Mourad Sini. The Green function of the interior transmission problem and its applications. Inverse Problems and Imaging, 2012, 6 (3) : 487-521. doi: 10.3934/ipi.2012.6.487 |
[4] |
Jongkeun Choi, Ki-Ahm Lee. The Green function for the Stokes system with measurable coefficients. Communications on Pure and Applied Analysis, 2017, 16 (6) : 1989-2022. doi: 10.3934/cpaa.2017098 |
[5] |
Peter Bella, Arianna Giunti. Green's function for elliptic systems: Moment bounds. Networks and Heterogeneous Media, 2018, 13 (1) : 155-176. doi: 10.3934/nhm.2018007 |
[6] |
Virginia Agostiniani, Rolando Magnanini. Symmetries in an overdetermined problem for the Green's function. Discrete and Continuous Dynamical Systems - S, 2011, 4 (4) : 791-800. doi: 10.3934/dcdss.2011.4.791 |
[7] |
Sungwon Cho. Alternative proof for the existence of Green's function. Communications on Pure and Applied Analysis, 2011, 10 (4) : 1307-1314. doi: 10.3934/cpaa.2011.10.1307 |
[8] |
Jon Aaronson, Michael Bromberg, Nishant Chandgotia. Rational ergodicity of step function skew products. Journal of Modern Dynamics, 2018, 13: 1-42. doi: 10.3934/jmd.2018012 |
[9] |
P.E. Kloeden, Victor S. Kozyakin. The perturbation of attractors of skew-product flows with a shadowing driving system. Discrete and Continuous Dynamical Systems, 2001, 7 (4) : 883-893. doi: 10.3934/dcds.2001.7.883 |
[10] |
Saša Kocić. Reducibility of skew-product systems with multidimensional Brjuno base flows. Discrete and Continuous Dynamical Systems, 2011, 29 (1) : 261-283. doi: 10.3934/dcds.2011.29.261 |
[11] |
Tomás Caraballo, Alexandre N. Carvalho, Henrique B. da Costa, José A. Langa. Equi-attraction and continuity of attractors for skew-product semiflows. Discrete and Continuous Dynamical Systems - B, 2016, 21 (9) : 2949-2967. doi: 10.3934/dcdsb.2016081 |
[12] |
Julia Brettschneider. On uniform convergence in ergodic theorems for a class of skew product transformations. Discrete and Continuous Dynamical Systems, 2011, 29 (3) : 873-891. doi: 10.3934/dcds.2011.29.873 |
[13] |
Xiaoxi Zhu, Kai Liu, Miaomiao Wang, Rui Zhang, Minglun Ren. Product line extension with a green added product: Impacts of segmented consumer preference on supply chain improvement and consumer surplus. Journal of Industrial and Management Optimization, 2022 doi: 10.3934/jimo.2022021 |
[14] |
Joel Coacalle, Andrew Raich. Compactness of the complex Green operator on non-pseudoconvex CR manifolds. Communications on Pure and Applied Analysis, 2021, 20 (6) : 2139-2154. doi: 10.3934/cpaa.2021061 |
[15] |
Núria Fagella, Àngel Jorba, Marc Jorba-Cuscó, Joan Carles Tatjer. Classification of linear skew-products of the complex plane and an affine route to fractalization. Discrete and Continuous Dynamical Systems, 2019, 39 (7) : 3767-3787. doi: 10.3934/dcds.2019153 |
[16] |
Zhi-Min Chen. Straightforward approximation of the translating and pulsating free surface Green function. Discrete and Continuous Dynamical Systems - B, 2014, 19 (9) : 2767-2783. doi: 10.3934/dcdsb.2014.19.2767 |
[17] |
Claudia Bucur. Some observations on the Green function for the ball in the fractional Laplace framework. Communications on Pure and Applied Analysis, 2016, 15 (2) : 657-699. doi: 10.3934/cpaa.2016.15.657 |
[18] |
Ali Unver, Christian Ringhofer, Dieter Armbruster. A hyperbolic relaxation model for product flow in complex production networks. Conference Publications, 2009, 2009 (Special) : 790-799. doi: 10.3934/proc.2009.2009.790 |
[19] |
Chirantan Mondal, Bibhas C. Giri. Investigating a green supply chain with product recycling under retailer's fairness behavior. Journal of Industrial and Management Optimization, 2021 doi: 10.3934/jimo.2021129 |
[20] |
Juan A. Calzada, Rafael Obaya, Ana M. Sanz. Continuous separation for monotone skew-product semiflows: From theoretical to numerical results. Discrete and Continuous Dynamical Systems - B, 2015, 20 (3) : 915-944. doi: 10.3934/dcdsb.2015.20.915 |
2020 Impact Factor: 1.392
Tools
Metrics
Other articles
by authors
[Back to Top]