论文标题
Hartman-Grobman定理的代数二分法
A Hartman-Grobman theorem for algebraic dichotomies
论文作者
论文摘要
代数二分法是指数二分法的概括（Lin，JDE2009）。本文给出了Hartman-Grobman线性化定理的版本，假设线性系统接受了代数二分法，该二分法概括了Palmer的线性化定理。此外，我们证明了线性化定理中的同构（并且具有Hölder连续逆）。与指数二分法相比，代数二分法更为复杂。指数二分法导致估计值$ \ int _ { - \ infty}^{t} e^{ - α（t-s）} ds $和$ \ int_ {t}^{+\ \ \ iffty} e^{ - α（s-α（s-α（s-t）} ds $。但是，代数二分法将使我们进入$ \ int _ { - \ infty}^{t} {t} \ left（\ frac {μ（t）} {μ（s）{μ（s）} \ right）^{ - α} ds $或$ \ int_ {t}^{+\ infty} \ left（\ frac {μ（s）} {μ（t）} \ right）^{ - α} ds $，其融合在Riemann的意义上是未知的。
Algebraic dichotomy is a generalization of an exponential dichotomy (Lin, JDE2009). This paper gives a version of Hartman-Grobman linearization theorem assuming that linear system admits an algebraic dichotomy, which generalizes the Palmer's linearization theorem. Besides, we prove that the homeomorphism in the linearization theorem (and has a Hölder continuous inverse). Comparing with exponential dichotomy, algebraic dichotomy is more complicate. The exponential dichotomy leads to the estimates $\int_{-\infty}^{t}e^{-α(t-s)}ds$ and $\int_{t}^{+\infty}e^{-α(s-t)}ds$ which are convergent. However, the algebraic dichotomy will leads us to $\int_{-\infty}^{t}\left(\frac{μ(t)}{μ(s)}\right)^{-α}ds$ or $\int_{t}^{+\infty}\left(\frac{μ(s)}{μ(t)}\right)^{-α}ds$, whose the convergence is unknown in the sense of Riemann.
