Embeddings of diffeomorphisms of the plane in regular iteration semigroups
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| 008 | 210128e20150201xx s 000 0 eng | ||
| 024 | 7 | 0 | |a 10.1007/s00010-014-0273-7 |2 doi |
| 035 | |a (NATIONALLICENCE)springer-10.1007/s00010-014-0273-7 | ||
| 245 | 0 | 0 | |a Embeddings of diffeomorphisms of the plane in regular iteration semigroups |h [Elektronische Daten] |c [Marek Zdun, Paweł Solarz] |
| 520 | 3 | |a 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. | |
| 540 | |a The Author(s), 2014 | ||
| 690 | 7 | |a Iteration semigroup |2 nationallicence | |
| 690 | 7 | |a Semiflows |2 nationallicence | |
| 690 | 7 | |a $${C^r_\delta}$$ C δ r -embedding |2 nationallicence | |
| 690 | 7 | |a Real logarithm of matrix |2 nationallicence | |
| 690 | 7 | |a Semigroup of matrices |2 nationallicence | |
| 690 | 7 | |a Functional equation |2 nationallicence | |
| 700 | 1 | |a Zdun |D Marek |u Institute of Mathematics, Pedagogical University, ul. Podchora̧żych 2, 30-084, Kraków, Poland |4 aut | |
| 700 | 1 | |a Solarz |D Paweł |u Institute of Mathematics, Pedagogical University, ul. Podchora̧żych 2, 30-084, Kraków, Poland |4 aut | |
| 773 | 0 | |t Aequationes mathematicae |d Springer Basel |g 89/1(2015-02-01), 149-160 |x 0001-9054 |q 89:1<149 |1 2015 |2 89 |o 10 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/s00010-014-0273-7 |q text/html |z Onlinezugriff via DOI |
| 898 | |a BK010053 |b XK010053 |c XK010000 | ||
| 900 | 7 | |a Metadata rights reserved |b Springer special CC-BY-NC licence |2 nationallicence | |
| 908 | |D 1 |a research-article |2 jats | ||
| 949 | |B NATIONALLICENCE |F NATIONALLICENCE |b NL-springer | ||
| 950 | |B NATIONALLICENCE |P 856 |E 40 |u https://doi.org/10.1007/s00010-014-0273-7 |q text/html |z Onlinezugriff via DOI | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Zdun |D Marek |u Institute of Mathematics, Pedagogical University, ul. Podchora̧żych 2, 30-084, Kraków, Poland |4 aut | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Solarz |D Paweł |u Institute of Mathematics, Pedagogical University, ul. Podchora̧żych 2, 30-084, Kraków, Poland |4 aut | ||
| 950 | |B NATIONALLICENCE |P 773 |E 0- |t Aequationes mathematicae |d Springer Basel |g 89/1(2015-02-01), 149-160 |x 0001-9054 |q 89:1<149 |1 2015 |2 89 |o 10 | ||