The well-known Hartman-Grobman Theorem says that a C~1 hyperbolic diffeomorphism F can be locally linearized by a homeomorphismΦ.For parameterized systems F_(θ),known results show that the corresponding homeomorphi...The well-known Hartman-Grobman Theorem says that a C~1 hyperbolic diffeomorphism F can be locally linearized by a homeomorphismΦ.For parameterized systems F_(θ),known results show that the corresponding homeomorphismsΦ_(θ)exist uniquely in a functional space equipped with the supremum norm and depend continuously on the parameterθ.In this paper,we further extend the results to Holder dependence ofΦ_(θ)onθby Pugh's strategy,but introducing a kind of special Holder norm instead of the usual supremum norm in the proof to control the linear parts of F_(θ).This requires a new Holder linearization result for every F_(θ).展开更多
基金supported by NSFC(Grant No.11671061)NSF-CQ(Grant No.cstc2018kjcxljrc0049)supported by NSF-CQ(Grant No.cstc2018jcyj AX0418)。
文摘The well-known Hartman-Grobman Theorem says that a C~1 hyperbolic diffeomorphism F can be locally linearized by a homeomorphismΦ.For parameterized systems F_(θ),known results show that the corresponding homeomorphismsΦ_(θ)exist uniquely in a functional space equipped with the supremum norm and depend continuously on the parameterθ.In this paper,we further extend the results to Holder dependence ofΦ_(θ)onθby Pugh's strategy,but introducing a kind of special Holder norm instead of the usual supremum norm in the proof to control the linear parts of F_(θ).This requires a new Holder linearization result for every F_(θ).
