Vanishing cycles for analytic maps

1991 ◽  
pp. 221-234 ◽  
Author(s):  
David Mond
Keyword(s):  
Vanishing Cycles ◽  
Analytic Maps

Fixed Points of Expansive Analytic Maps (II)

1992 ◽  
Author(s):  
Walter O. Egerland ◽  
Charles E. Hansen
Keyword(s):  
Fixed Points ◽  
Analytic Maps

scholarly journals Conjectures on Stably Newton Degenerate Singularities

2021 ◽  
Author(s):  
Jan Stevens
Keyword(s):  
Characteristic Zero ◽  
Arbitrary Number ◽  
Milnor Number ◽  
Plane Curves ◽  
Newton Diagram ◽  
Finite Characteristic ◽  
Vanishing Cycles

AbstractWe discuss a problem of Arnold, whether every function is stably equivalent to one which is non-degenerate for its Newton diagram. We argue that the answer is negative. We describe a method to make functions non-degenerate after stabilisation and give examples of singularities where this method does not work. We conjecture that they are in fact stably degenerate, that is not stably equivalent to non-degenerate functions.We review the various non-degeneracy concepts in the literature. For finite characteristic, we conjecture that there are no wild vanishing cycles for non-degenerate singularities. This implies that the simplest example of singularities with finite Milnor number, $$x^p+x^q$$ x p + x q in characteristic p, is not stably equivalent to a non-degenerate function. We argue that irreducible plane curves with an arbitrary number of Puiseux pairs (in characteristic zero) are stably non-degenerate. As the stabilisation involves many variables, it becomes very difficult to determine the Newton diagram in general, but the form of the equations indicates that the defining functions are non-degenerate.

scholarly journals Algebraicity of analytic maps to a hyperbolic variety

2020 ◽  
Vol 293 (8) ◽  
pp. 1490-1504 ◽  
Author(s):  
Ariyan Javanpeykar ◽  
Robert Kucharczyk
Keyword(s):  
Analytic Maps

On translations of the images of analytic maps

1994 ◽  
Vol 24 (3-4) ◽  
pp. 205-208
Author(s):  
Ian Graham ◽  
Drop Varolin
Keyword(s):  
Analytic Maps

scholarly journals Continued g-Fractions and Geometry of Bounded Analytic Maps

2013 ◽  
Vol 20 (2) ◽  
pp. 181-196
Author(s):  
Alexei Tsygvintsev
Keyword(s):  
Analytic Maps

scholarly journals Random iteration of analytic maps

2004 ◽  
Vol 24 (3) ◽  
pp. 659-675 ◽  
Author(s):  
A. F. BEARDON ◽  
T. K. CARNE ◽  
D. MINDA ◽  
T. W. NG
Keyword(s):  
Random Iteration ◽  
Analytic Maps

scholarly journals On the Lê-Milnor fibration for real analytic maps

2016 ◽  
Vol 290 (2-3) ◽  
pp. 382-392 ◽  
Author(s):  
Aurélio Menegon Neto ◽  
José Seade
Keyword(s):  
Milnor Fibration ◽  
Real Analytic ◽  
Analytic Maps

Homeomorphic Analytic Maps into the Maximal Ideal Space of H∞

1999 ◽  
Vol 51 (1) ◽  
pp. 147-163 ◽  
Author(s):  
Daniel Suárez
Keyword(s):  
Maximal Ideal ◽  
Maximal Ideal Space ◽  
Ideal Space ◽  
Gleason Part ◽  
Interpolating Sequences ◽  
Closed Subalgebra ◽  
Analytic Maps ◽  
The Ideal

AbstractLet m be a point of the maximal ideal space of H∞ with nontrivial Gleason part P(m). If Lm : D → P(m) is the Hoffman map, we show that H∞ ° Lm is a closed subalgebra of H∞. We characterize the points m for which Lm is a homeomorphism in terms of interpolating sequences, and we show that in this case H∞ ° Lm coincides with H∞. Also, if Im is the ideal of functions in H∞ that identically vanish on P(m), we estimate the distance of any f ϵ H∞ to Im.

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