caa a22 4500 605508011 CHVBK 20210128100634.0 cr unu---uuuuu 210128e20150201xx s 000 0 eng 10.1007/s00010-014-0273-7 doi (NATIONALLICENCE)springer-10.1007/s00010-014-0273-7 Embeddings of diffeomorphisms of the plane in regular iteration semigroups [Elektronische Daten] [Marek Zdun, Paweł Solarz] We give the full description of the $${C^r_\delta}$$ C δ r embeddings of a given diffeomorphism $${F \colon \mathbb{R}^2 \supset U \to \mathbb{R}^2}$$ F : R 2 ⊃ U → R 2 of class C r such that F(0) = 0 and $${d^{(r)}F(x) = d^{(r)}F(0) + O(\|x\|^{\delta}), \ \|x\|\to 0}$$ d ( r ) F ( x ) = d ( r ) F ( 0 ) + O ( ‖ x ‖ δ ) , ‖ x ‖ → 0 with a hyperbolic fixed point. That is we determine all families of $${C^r_\delta}$$ C δ r diffeomorphisms of the plane defined in a neighbourhood of the origin such that $${F^t\circ F^s=F^{t+s}}$$ F t ∘ F s = F t + s , t,s ≥ 0, F 1=F and the mapping $${t \mapsto F^t(x)}$$ t ↦ F t ( x ) is continuous. To describe these semigroups we determine the real logarithms and all continuous groups of the real non-singular matrices. The Author(s), 2014 Iteration semigroup nationallicence Semiflows nationallicence $${C^r_\delta}$$ C δ r -embedding nationallicence Real logarithm of matrix nationallicence Semigroup of matrices nationallicence Functional equation nationallicence Zdun Marek Institute of Mathematics, Pedagogical University, ul. Podchora̧żych 2, 30-084, Kraków, Poland aut Solarz Paweł Institute of Mathematics, Pedagogical University, ul. Podchora̧żych 2, 30-084, Kraków, Poland aut Aequationes mathematicae Springer Basel 89/1(2015-02-01), 149-160 0001-9054 89:1<149 2015 89 10 https://doi.org/10.1007/s00010-014-0273-7 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s00010-014-0273-7 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Zdun Marek Institute of Mathematics, Pedagogical University, ul. Podchora̧żych 2, 30-084, Kraków, Poland aut NATIONALLICENCE 700 1- Solarz Paweł Institute of Mathematics, Pedagogical University, ul. Podchora̧żych 2, 30-084, Kraków, Poland aut NATIONALLICENCE 773 0- Aequationes mathematicae Springer Basel 89/1(2015-02-01), 149-160 0001-9054 89:1<149 2015 89 10