On the Combinatorics of Fibonacci-Like Non-renormalizable Maps  

作　　者：Haoyang Ji Simin Li 

机构地区：[1]School of Mathematical Sciences,University of Science and Technology of China,Hefei 230026,People’s Republic of China

出　　处：《Communications in Mathematics and Statistics》2020年第4期473-496,共24页数学与统计通讯（英文）

基　　金：Simin Li is supported by NSFC grant 11731003.

摘　　要：In this paper,we extend Fibonacci unimodal map to a wider class.We describe the combinatorial property of thesemaps by first return map and principal nest.We give the sufficient and necessary condition for the existence of this class ofmaps.Moreover,for maps with’bounded combinatorics’,we prove that they have no absolutely continuous invariant probability measure when the critical order ι is sufficiently large;for maps with reluctantly recurrent critical point,we prove they have absolutely continuous invariant probability measure whenever the critical order ι>1.

关 键 词：FIBONACCI Principal nest Invariantmeasure Generalized renormalization 

分 类 号：O17[理学—数学]