000			01972n a2200289#a 4500
001			38624
003			P5A
005			20221213140615.0
007			cr cuuuuuauuuu
008			180906s2018 bl por d
035			_aocm51338542
040			_aP5A _cP5A
082	0	4	_acs
090			_acs
100	1		_aZamudio Espinosa, Alex Mauricio _910312
245	1	0	_aHausdorff dimension for projections of dynamically defined complex Cantor sets.
260			_aRio de Janeiro: _bIMPA, _c2018.
300			_avideo online
500			_aSeminários de Sistemas Dinâmicos.
505	1		_aResumo: A classical theorem of Marstrand states that for any Borel subset F ?R2 HD(p?(F)) = min{1,HD(F)}, for almost all projection p?(x,y) = x+?y (with respect to Lebesgue measure in ?). Moreira was able to improve this theorem in the particular context of dynamically defined Cantor sets. He proved that given dynamically defined Cantor sets K1,K2 ? R satisfying some generic hypothesis one has HD(K1 +?·K2) =min{1,HD(K1)+HD(K2)}, for all ?= 0. We will talk about how Moreiras ideas can be generalized to Cantor sets in the complex plane, in particular we will have a similar formula which holds for dynamically defined complex Cantor sets. In particular, this Cantor sets include Julia sets associated to quadratic maps Qc(z) = z2 + c when the parameter c is not in the Mandelbrot set.
650	0	4	_aMatematica. _2larpcal _919899
650	0	4	_aSistemas dinamicos. _913212
697			_aCongressos e Seminários. _923755
700	1		_aMoreira, Carlos Gustavo T. de A. _912783
856	4		_zVIDEO _uhttps://www.youtube.com/watch?v=NAJnCci5NpY&list=PLo4jXE-LdDTQtj15bpgTQ_LK7x1n5FDrw&t=2s&index=2
942			_2ddc _cBK
999			_aHAUSDORFF dimension for projections of dynamically defined complex Cantor sets. Rio de Janeiro: IMPA, 2018. video online. Disponível em: https://www.youtube.com/watch?v=NAJnCci5NpY&list=PLo4jXE-LdDTQtj15bpgTQ_LK7x1n5FDrw&t=2s&index=2. Acesso em: 30 ago. 2017. _c37247 _d37247