The complex potential generated by the maximal measure for a family of rational maps.

DOI10.1007/BF01019717zbMath1084.37514MaRDI QIDQ1963501

Artur Oscar Lopes

Publication date: 2 February 2000

Published in: Journal of Statistical Physics (Search for Journal in Brave)

zbMATH Keywords

Julia setscomplex potentialrational mapstheory of momentsbalanced measureMaximal measure

Mathematics Subject Classification ID

Entropy and other invariants (28D20) Functional equations in the complex plane, iteration and composition of analytic functions of one complex variable (30D05) Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets (37F10)

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Cites Work

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• The dimension of the maximal measure for a polynomial map
• Mellin transforms associated with Julia sets and physical applications
• An invariant measure for rational maps
• Equilibrium measures for rational maps
• Orthogonal polynomials associated with invariant measures on Julia sets