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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

On global linearization of planar involutions

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Author(s):
Pires, Benito [1] ; Teixeira, Marco Antonio [2]
Total Authors: 2
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
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 type: 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 type: Research Projects - Thematic Grants
FAPESP's process: 08/02841-4 - Topology, geometry and ergodic theory of dynamical systems
Grantee:Jorge Manuel Sotomayor Tello
Support type: Research Projects - Thematic Grants