The dynamics of holomorphic maps near curves of fixed points
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 2 (2003) no. 3, p. 493-520
Let M be a two-dimensional complex manifold and f:MM a holomorphic map. Let SM be a curve made of fixed points of f, i.e.  Fix (f)=S. We study the dynamics near S in case f acts as the identity on the normal bundle of the regular part of S. Besides results of local nature, we prove that if S is a globally and locally irreducible compact curve such that S·S<0 then there exists a point pS and a holomorphic f-invariant curve with p on the boundary which is attracted by p under the action of f. These results are achieved introducing and studying a family of local holomorphic foliations related to f near S.
Classification:  32H50,  37F99,  32S45,  32S65
@article{ASNSP_2003_5_2_3_493_0,
     author = {Bracci, Filippo},
     title = {The dynamics of holomorphic maps near curves of fixed points},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     publisher = {Scuola normale superiore},
     volume = {Ser. 5, 2},
     number = {3},
     year = {2003},
     pages = {493-520},
     zbl = {1170.32311},
     mrnumber = {2020858},
     language = {en},
     url = {http://www.numdam.org/item/ASNSP_2003_5_2_3_493_0}
}
Bracci, Filippo. The dynamics of holomorphic maps near curves of fixed points. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 2 (2003) no. 3, pp. 493-520. http://www.numdam.org/item/ASNSP_2003_5_2_3_493_0/

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