Dynamics of polynomial maps on {${\bf C}\sp 2$} whose all unbounded orbits converge to one point

Shinohara, Tomoko

Kodai Math. J., Tome 25 (2002) no. 2, p. 15-42 / Harvested from Project Euclid

Résumé

In this paper, we study a family of iteration of polynomial map on the 2-dimensional complex Euclidean space {${\bf C}\sp 2$} whose all unbounded orbits converge to one point of the line at infinity in the 2-dimensional complex projective space {${\bf P}\sp 2$}. In particular, we show some sufficient condition for the Lebesgue measure of its Julia set to be equal to 0.

Publié le : 2002-05-14
Classification: 37F10, 32H50

@article{1106171073,
     author = {Shinohara, Tomoko},
     title = {Dynamics of polynomial maps on {${\bf C}\sp 2$} whose all unbounded orbits converge to one point},
     journal = {Kodai Math. J.},
     volume = {25},
     number = {2},
     year = {2002},
     pages = { 15-42},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1106171073}
}

Shinohara, Tomoko. Dynamics of polynomial maps on {${\bf C}\sp 2$} whose all unbounded orbits converge to one point. Kodai Math. J., Tome 25 (2002) no. 2, pp.  15-42. http://gdmltest.u-ga.fr/item/1106171073/