scholarly journals Bifurcation locus and branches at infinity of a polynomial $$f:\mathbb {C}^2\rightarrow \mathbb {C}$$ f : C 2 → C

2014 ◽  
Vol 361 (3-4) ◽  
pp. 1049-1054 ◽  
Author(s):  
Zbigniew Jelonek ◽  
Mihai Tibăr
Keyword(s):  
Bifurcation Locus

scholarly journals Distribution of polynomials with cycles of a given multiplier

2011 ◽  
Vol 201 ◽  
pp. 23-43 ◽  
Author(s):  
Giovanni Bassanelli ◽  
François Berteloot
Keyword(s):  
Quadratic Polynomials ◽  
Bifurcation Locus

AbstractIn the space of degreedpolynomials, the hypersurfaces defined by the existence of a cycle of periodnand multipliereiθare known to be contained in the bifurcation locus. We prove that these hypersurfaces equidistribute the bifurcation current. This is a new result, even for the space of quadratic polynomials.

scholarly journals Lattès maps and the interior of the bifurcation locus

2019 ◽  
Vol 15 (0) ◽  
pp. 95-130
Author(s):  
Sébastien Biebler ◽  
Keyword(s):  
Bifurcation Locus

scholarly journals Toward Effective Detection of the Bifurcation Locus of Real Polynomial Maps

2016 ◽  
Vol 17 (3) ◽  
pp. 837-849 ◽  
Author(s):  
Luis Renato G. Dias ◽  
Susumu Tanabé ◽  
Mihai Tibăr
Keyword(s):  
Real Polynomial ◽  
Bifurcation Locus ◽  
Polynomial Maps ◽  
Real Polynomial Maps

scholarly journals Distribution of polynomials with cycles of a given multiplier

2011 ◽  
Vol 201 ◽  
pp. 23-43 ◽  
Author(s):  
Giovanni Bassanelli ◽  
François Berteloot
Keyword(s):  
Quadratic Polynomials ◽  
Bifurcation Locus

AbstractIn the space of degree d polynomials, the hypersurfaces defined by the existence of a cycle of period n and multiplier eiθ are known to be contained in the bifurcation locus. We prove that these hypersurfaces equidistribute the bifurcation current. This is a new result, even for the space of quadratic polynomials.

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