与位置相关的幂等迭代函数系统的不变度量

IF 1.4 3区数学 Q1 MATHEMATICS

Journal of Fixed Point Theory and Applications Pub Date : 2024-05-11 DOI:10.1007/s11784-024-01109-8

Jairo K. Mengue, Elismar R. Oliveira

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引用次数: 0

摘要

我们研究了定义在紧凑度量空间中的地方依赖幂迭代函数系统的不变幂概率集。利用动力学系统中的著名思想，如马内势和奥布里集，我们提供了此类幂等概率密度的完整表征。作为应用，我们提供了一类模糊迭代函数系统吸引子的替代公式。

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Invariant measures for place-dependent idempotent iterated function systems

We study the set of invariant idempotent probabilities for place-dependent idempotent iterated function systems defined in compact metric spaces. Using well-known ideas from dynamical systems, such as the Mañé potential and the Aubry set, we provide a complete characterization of the densities of such idempotent probabilities. As an application, we provide an alternative formula for the attractor of a class of fuzzy iterated function systems.

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来源期刊

Journal of Fixed Point Theory and Applications 数学-数学

CiteScore

3.10

自引率

5.60%

发文量

审稿时长

>12 weeks

期刊介绍： The Journal of Fixed Point Theory and Applications (JFPTA) provides a publication forum for an important research in all disciplines in which the use of tools of fixed point theory plays an essential role. Research topics include but are not limited to: (i) New developments in fixed point theory as well as in related topological methods, in particular: Degree and fixed point index for various types of maps, Algebraic topology methods in the context of the Leray-Schauder theory, Lefschetz and Nielsen theories, Borsuk-Ulam type results, Vietoris fractions and fixed points for set-valued maps. (ii) Ramifications to global analysis, dynamical systems and symplectic topology, in particular: Degree and Conley Index in the study of non-linear phenomena, Lusternik-Schnirelmann and Morse theoretic methods, Floer Homology and Hamiltonian Systems, Elliptic complexes and the Atiyah-Bott fixed point theorem, Symplectic fixed point theorems and results related to the Arnold Conjecture. (iii) Significant applications in nonlinear analysis, mathematical economics and computation theory, in particular: Bifurcation theory and non-linear PDE-s, Convex analysis and variational inequalities, KKM-maps, theory of games and economics, Fixed point algorithms for computing fixed points. (iv) Contributions to important problems in geometry, fluid dynamics and mathematical physics, in particular: Global Riemannian geometry, Nonlinear problems in fluid mechanics.