Parabolic manifolds for semi-attractive holomorphic germs

Rivi, Marzia

doi:10.1307/mmj/1008719770

Cited by 18 publications

(9 citation statements)

References 5 publications

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“…Similar results hold for quasi-parabolic maps (see [R3]) and semi-attractive maps (see e.g. [F2,U,H1,Ri,R4]). Recall that a holomorphic map f is said to be semi-attractive at 0 if df 0 = Diag(I l , A), where I l is the identity matrix with size 1 ≤ l ≤ n − 1 and the eigenvalues of A all have modulus less than one.…”

Section: The Matrixsupporting

confidence: 66%

A Brief Survey on Local Holomorphic Dynamics in Higher Dimensions

Rong

2015

Springer Proceedings in Mathematics &Amp; Statistics

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Section: The Matrixsupporting

confidence: 66%

A Brief Survey on Local Holomorphic Dynamics in Higher Dimensions

Rong

2015

Springer Proceedings in Mathematics &Amp; Statistics

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“…She proved that either there exists a curve of fixed points or there exist attracting open petals. Such a result has been later generalized by Rivi [23].…”

Section: Introductionmentioning

confidence: 70%

Dynamics of one-resonant biholomorphisms

Bracci¹,

Zaitsev²

2012

J. Eur. Math. Soc.

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Our first main result is a construction of a simple formal normal form for holomorphic diffeomorphisms in C n whose differentials have one-dimensional family of resonances in the first m eigenvalues, m ≤ n (but more resonances are allowed for other eigenvalues). Next, we provide invariants and give conditions for the existence of basins of attraction. Finally, we give applications and examples demonstrating the sharpness of our conditions.

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“…By [Ri,Proposition 3.1], the class of similarity of the matrix Γ is invariant under changes of coordinates. Therefore, the eigenvalues of Γ are invariants associated to [v].…”

Section: The Operator Tmentioning

confidence: 99%

Parabolic manifolds for semi-attractive analytic transformations of 𝐂ⁿ

Rong

2011

Trans. Amer. Math. Soc.

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Abstract. We study the local dynamics of semi-attractive analytic transformations of C n . Under certain assumptions, Rivi showed the existence of parabolic manifolds of dimension m + 1, where m is the number of eigenvalues with modulus strictly less than one. Assuming moreover that certain matrix has p eigenvalues with positive real part, we show the existence of parabolic manifolds of dimension m + p + 1.

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Parabolic manifolds for semi-attractive holomorphic germs

Cited by 18 publications

References 5 publications

A Brief Survey on Local Holomorphic Dynamics in Higher Dimensions

A Brief Survey on Local Holomorphic Dynamics in Higher Dimensions

Dynamics of one-resonant biholomorphisms

Parabolic manifolds for semi-attractive analytic transformations of 𝐂ⁿ

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