Geodesic
On the attractors of Feigenbaum maps
Guifeng Huang1 ; Lidong Wang2
1 Department of Basic Science Dalian Naval Academy 116018 Dalian, Liaoning, China
2 Department of Mathematics Dalian Nationalities University 116600 Dalian, Liaoning, China
Annales Polonici Mathematici, Tome 110 (2014) no. 1, pp. 55-62

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

A solution of the Feigenbaum functional equation is called a Feigenbaum map. We investigate the likely limit set (i.e. the maximal attractor in the sense of Milnor) of a non-unimodal Feigenbaum map, prove that it is a minimal set that attracts almost all points, and then estimate its Hausdorff dimension. Finally, for every $s\in (0,1)$, we construct a non-unimodal Feigenbaum map with a likely limit set whose Hausdorff dimension is $s$.
DOI : 10.4064/ap110-1-5
Keywords: solution feigenbaum functional equation called feigenbaum map investigate likely limit set maximal attractor sense milnor non unimodal feigenbaum map prove minimal set attracts almost points estimate its hausdorff dimension finally every construct non unimodal feigenbaum map likely limit set whose hausdorff dimension

Guifeng Huang 1 ; Lidong Wang 2

1 Department of Basic Science Dalian Naval Academy 116018 Dalian, Liaoning, China
2 Department of Mathematics Dalian Nationalities University 116600 Dalian, Liaoning, China 
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Guifeng Huang; Lidong Wang. On the attractors of Feigenbaum maps. Annales Polonici Mathematici, Tome 110 (2014) no. 1, pp. 55-62. doi: 10.4064/ap110-1-5

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