Constructing chaotic functions on nonorientable surfaces via interval maps
TURKISH JOURNAL OF MATHEMATICS, sa.50, ss.1095-1107, 2026 (SCI-Expanded, Scopus, TRDizin)
- Yayın Türü: Makale / Tam Makale
- Basım Tarihi: 2026
- Doi Numarası: 10.55730/1300-0098.3785
- Dergi Adı: TURKISH JOURNAL OF MATHEMATICS
- Derginin Tarandığı İndeksler: Academic Search Ultimate (EBSCO), Scopus, Science Citation Index Expanded (SCI-EXPANDED), MathSciNet, zbMATH, TR DİZİN (ULAKBİM)
- Sayfa Sayıları: ss.1095-1107
- Karadeniz Teknik Üniversitesi Adresli: Evet
Özet
We construct chaotic functions on the nonorientable surfaces known as the Möbius strip, Klein bottle, and projective plane, which are well-known objects in topology. As is customary, these surfaces are obtained as quotient spaces of the unit square [0,1]×[0,1]. To construct chaotic functions on these surfaces, we first obtain chaotic functions on the unit square using the product method. In the product method, we utilize well-known chaotic maps on the unit interval, namely the logistic and tent maps. We then observe that each Cartesian product map induces a well-defined chaotic function on the corresponding surfaces. We also point out that our construction method is applicable to other interval maps that share symmetry properties similar to those of the logistic and tent maps. Furthermore, by determining the topological entropy of these chaotic functions, we show that they are also chaotic in the Li–Yorke sense.