Iterated Function Systems and Lojasiewicz-Siciak Condition of Green's Function

作者：Bialas Ciez Leokadia; Kosek Marta^*

来源：Potential Analysis, 2011, 34(3): 207-221.

DOI：10.1007/s11118-010-9188-7

• Iterated function system
• Similarity
• Attractor
• Green's function
• Lojasiewicz type inequality

A compact set K subset of C-N satisfies (LS) if it is polynomially convex and there exist constants B, beta > 0 such that V-K (z) >= B (dist(z, K))(beta) if dist (z, K) <= 1, (LS) where V (K) denotes the pluricomplex Green's function of the set K. The property was defined by Gendre and used together with the Holder continuity of the Green's function in approximation on the set K. We construct a family of uniformly perfect totally disconnected planar attractors of iterated function systems which have the (AS) property.

• 出版日期2011-4