| Full text | |
| Author(s): |
Total Authors: 2
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| Affiliation: | [1] Univ Sao Paulo, Fac Filosofia Ciencias & Letras, Dept Comp & Matemat, BR-14040901 Ribeirao Preto, SP - Brazil
[2] Univ Estadual Campinas UNICAMP, Dept Matemat, BR-13083970 Campinas, SP - Brazil
Total Affiliations: 2
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| Document type: | Journal article |
| Source: | BULLETIN OF THE BRAZILIAN MATHEMATICAL SOCIETY; v. 43, n. 4, p. 637-653, DEC 2012. |
| Web of Science Citations: | 0 |
| Abstract | |
Let phi: a{''}e(2) -> a{''}e(2) be an orientation-preserving C (1) involution such that phi(0) = 0. Let Spc(phi) = [Eigenvalues of D phi(p) | p a a{''}e(2)]. We prove that if Spc(phi) aS, a{''}e or Spc(phi) a (c) {[}1, 1 + epsilon) = a... for some epsilon > 0, then phi is globally C (1) conjugate to the linear involution D phi(0) via the conjugacy h = (I + D phi(0)phi)/2,where I: a{''}e(2) -> a{''}e(2) is the identity map. Similarly, we prove that if phi is an orientation-reversing C (1) involution such that phi(0) = 0 and Trace (D phi(0)D phi(p) > - 1 for all p a a{''}e(2), then phi is globally C (1) conjugate to the linear involution D phi(0) via the conjugacy h. Finally, we show that h may fail to be a global linearization of phi if the above conditions are not fulfilled. (AU) | |
| FAPESP's process: | 09/02380-0 - Flows on surfaces and exchange transformations |
| Grantee: | Benito Frazao Pires |
| Support Opportunities: | Research Grants - Young Investigators Grants |
| FAPESP's process: | 07/06896-5 - Geometry of control, dynamical and stochastic systems |
| Grantee: | Luiz Antonio Barrera San Martin |
| Support Opportunities: | Research Projects - Thematic Grants |
| FAPESP's process: | 08/02841-4 - Topology, geometry and ergodic theory of dynamical systems |
| Grantee: | Jorge Manuel Sotomayor Tello |
| Support Opportunities: | Research Projects - Thematic Grants |