Holomorphic Dynamical Systems

Abstract

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Torus Actions in the Normalization Problem

“…Therefore x ∈ Q if and only if M, η (2) = · · · = M, η (r) = 0, and moreover in that case (1) . (1) | M ∈ Z n , M, η (2) = · · · = M, η (r) = 0}…”

“…, (η (r) ) T . But this implies that the linear form (η (1) ) T is a Q-linear combination of (η (2) ) T , . .…”

“…, (η (r) ) T . It is easy to see that this implies that the kernel in Q n of the linear form (η (1) ) T contains the intersection of the kernels in Q n of the linear forms (η (2) ) T , . .…”

“…dynamics (see [1,2], and [6] for general surveys on this topic) is when f is holomorphically linearizable, i.e., when there exists a local holomorphic change of coordinates such that f is conjugated to its linear part. The answer to this question depends on the set of eigenvalues of df O , usually called the spectrum of df O .…”

Recent results on iteration theory: iteration groups and semigroups in the real case

“…This is a very large domain and the subject is beyond the scope of this paper. A lot of information and references of this topic can be found in the survey articles [1,120,121]. We focus here on the selected problems of iteration theory strictly related to functional equations.…”