Dynamics of rational maps: a current on the bifurcation locus

By Laura Demarco. 2001

83 citations recorded by the source corpus.

Subfields: Geometry and Topology, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/8ded648dc35d680dac9684fa1cad70179613ceb4

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Geometry and Topology

1. Franccois Berteloot
2. Matthew Baker
3. C. Favre
4. Romain Dujardin
5. G. Bassanelli
6. Laura De Marco
7. Laura Demarco
8. Mattias Jonsson

In Mathematical Physics

1. Franccois Berteloot
2. C. Favre
3. Romain Dujardin
4. Matthew Baker
5. G. Bassanelli
6. Laura De Marco
7. Mattias Jonsson
8. Laura Demarco

In Statistical and Nonlinear Physics

1. Franccois Berteloot
2. Romain Dujardin
3. C. Favre
4. G. Bassanelli
5. Laura De Marco
6. Matthew Baker
7. T. Dinh
8. N. Sibony

Citations in the corpus

• Bifurcation currents in holomorphic dynamics on ${\bf P}^k$ (2005, background): “More recently, DeMarco ([9], [8]) has obtained a generalization of this formula to rational maps of P1.”
• Distribution of rational maps with a preperiodic critical point (2006, background): “Following L.DeMarco [ DeM1 ] it is possible to associate a natural positive closed (1,1) current T to a marked critical point λ 7→ c(λ).”
• Distribution of postcritically finite polynomials (2013, unknown): “DeMarco [De] proved that, in any holomorphic family of rational maps, the bifurcation locus is the support of a closed positive (1, 1)-current with continuous potential.”
• Bifurcation Currents in Holomorphic Families of Rational Maps (2012, background): “The following result has been originally proved by DeMarco in [20], [21].”
• Bifurcation currents in holomorphic dynamics on (2007, background): “where L(p) is the Lyapunov exponent of p with respect to its equilibrium measure, Gp its Green function and cj are the critical points of p. More recently, DeMarco ([9], [ 8 ]) has obtained a generalization of this formula to rational maps of P 1 . She also used her formula to show that, for a holom”
• SPECIAL CURVES AND POSTCRITICALLY FINITE POLYNOMIALS (2012, background): “ll t. In that case, the support of acoincides with the activity locus of the critical point, the set of parameters where the critical point is \passing through" the Julia set of f t [MSS]. See [De1] and [DF] for background on bifurcation currents. Similarly for any marked point, the support of”