Fixed points of anti‐attracting maps and eigenforms on fractals
نویسندگان
چکیده
An important problem in analysis on fractals is the existence of a self-similar energy finitely ramified fractals. The energies are constructed terms eigenforms, that is, eigenvectors special nonlinear operator. Previous results by C. Sabot and V. Metz give conditions for an eigenform. In this paper, I prove type result different way. proof given paper based general fixed-point theorem anti-attracting maps convex set.
منابع مشابه
Othogonality and Fixed Points of Nonexpansive Maps
The concept of weakorthogonality for a Banach lattice is examined. A proof that in such a lattice non expansive self maps of a non empty weakly compact convex set have fixed points is outlined. A geometric generalization of weakorthogonality is introduced and related to the Opial condition. AMS subject classification: 47H10
متن کاملFixed Points and Periodic Points of Semiflows of Holomorphic Maps
Let φ be a semiflow of holomorphic maps of a bounded domain D in a complex Banach space. The general question arises under which conditions the existence of a periodic orbit of φ implies that φ itself is periodic. An answer is provided, in the first part of this paper, in the case in which D is the open unit ball of a J∗-algebra and φ acts isometrically. More precise results are provided when t...
متن کاملFractals as Fixed Points of Iterated Function Systems
This paper discusses one method of producing fractals, namely that of iterated function systems. We first establish the tools of Hausdorff measure and Hausdorff dimension to analyze fractals, as well as some concepts in the theory of metric spaces. The latter allows us to prove the existence and uniqueness of fractals as fixed points of iterated function systems. We discuss the connection betwe...
متن کاملCommon fixed points of four maps using generalized weak contractivity and well-posedness
In this paper, we introduce the concept of generalized -contractivityof a pair of maps w.r.t. another pair. We establish a common fixed point result fortwo pairs of self-mappings, when one of these pairs is generalized -contractionw.r.t. the other and study the well-posedness of their fixed point problem. Inparticular, our fixed point result extends the main result of a recent paper ofQingnian ...
متن کاملCurves of fixed points of trace maps
We study curves of fixed points for certain diffeomorphisms of R3 that are induced by automorphisms of a trace algebra. We classify these curves. There is a function E which is invariant under all such trace maps and the level surfaces Et : E = t are invariant; a point of Et will be said to have level t . The surface E1 is significant. Then most fixed points onE1 are actually on a curve γ of fi...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Mathematische Nachrichten
سال: 2021
ISSN: ['1522-2616', '0025-584X']
DOI: https://doi.org/10.1002/mana.201800093