文摘
We consider a map of the unit square which is not 1–1, such as the memory map studied in Góra (Statistical and deterministic dynamics of maps with memory, http://arxiv.org/abs/1604.06991). Memory maps are defined as follows: \(x_{n+1}=M_{\alpha }(x_{n-1},x_{n})=\tau (\alpha \cdot x_{n}+(1-\alpha )\cdot x_{n-1}),\) where \(\tau \) is a one-dimensional map on \(I=[0,1]\) and \(0<\alpha <1\) determines how much memory is being used. In this paper we let \(\tau \) to be the symmetric tent map. To study the dynamics of \(M_\alpha \), we consider the two-dimensional map $$\begin{aligned} G_{\alpha }:[x_{n-1},x_{n}]\mapsto [x_{n},\tau (\alpha \cdot x_{n}+(1-\alpha )\cdot x_{n-1})]\, . \end{aligned}$$The map \(G_\alpha \) for \(\alpha \in (0,3/4]\) was studied in Góra (Statistical and deterministic dynamics of maps with memory, http://arxiv.org/abs/1604.06991). In this paper we prove that for \(\alpha \in (3/4,1)\) the map \(G_\alpha \) admits a singular Sinai-Ruelle-Bowen measure. 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Soc. 287(1), 41–48 (1985)ADSMathSciNetCrossRefMATHGoogle ScholarCopyright information© Springer Science+Business Media New York 2016Authors and AffiliationsPaweł Góra1Email authorView author's OrcID profileAbraham Boyarsky1Zhenyang Li21.Department of Mathematics and StatisticsConcordia UniversityMontrealCanada2.Department of MathematicsHonghe UniversityMengziChina About this article CrossMark Print ISSN 0022-4715 Online ISSN 1572-9613 Publisher Name Springer US About this journal Reprints and Permissions Article actions Export citation .RIS Papers Reference Manager RefWorks Zotero .ENW EndNote .BIB BibTeX JabRef Mendeley Share article Email Facebook Twitter LinkedIn Cookies We use cookies to improve your experience with our site. More information Accept Over 10 million scientific documents at your fingertips
