H2020Индивидуална стипендия2017–2019

CoTraDy · Combinatorics in Transcendental Dynamics

„Хоризонт 2020“ — Действия „Мария Склодовска-Кюри“

Период: 2017-09-01 → 2019-08-31
Финансиране от ЕС: 170 122 €
Участници: 1
Схема: MSCA-IF

Линиите свързват координатора с партньорите.

Накратко на български

Математическите динамични системи анализират как се променят абстрактни функции при многократно повтаряне, като например проследяват криви от точки, които се отдалечават от центъра. Тези проучвания помагат за подобряване на алгоритми като метода на Нютон, който се използва за намиране на корени на полиноми.

Този кратък обзор е генериран от изкуствен интелект

Кратко обяснение, генерирано от езиков модел по текста на CORDIS. Оригиналът е по-долу.

Резултати накратко

Combinatorics in Transcendental Dynamics

The topic of this project is in Dynamical System, a wide and variegated area of mathematics concerned with the study of the evolution of systems of any kind, from biological models to abstract mathematical systems. The main purpose of this project was to study a specific type of abstract system given by the iteration of some functions called entire transcendental maps, and to deepen our understanding of such systems by investigating specific subsystems (the 'curves escaping points', or 'rays') which can be correlated with other simple and well understood examples. This type of approach takes the name of 'combinatorial study'. This is a project in pure mathematics, so its direct impact for society in terms of research is long-term and difficult to predict. Other works concerning the dynamics of entire functions have proven useful in improving Newton's Method, a widely used algorithm to find roots of polynomials which has applications in several areas of science. As outreach activity we have planned and executed several conferences about fractals for high school students, which have been very successful. We believe that presenting female researchers in science to this particular type of public is important to promote female role models in science to teenagers, and encourages female students to pursue careers in STEM. The scientific objectives were to investigate the patterns arising from the aforementioned subsystems (the curves escaping points, or rays) and their relation to periodic points, that is, equilibrium states of the systems.

Текст от CORDIS, на английски · Данни: CORDIS, © Европейски съюз

Цел на проекта

Complex dynamics studies the evolution of a complex manifold under the action of a holomorphic map. In this proposal we study the dynamical systems generated by transcendental (either entire or meromorphic) maps acting on the complex plane. By using a wide range of classic and new techniques, we investigates epecially the combinatorics of these maps: that is to say, we build relations between the dynamics of the transcendental map on some specific subset of the complex plane and the dynamics of the shift map on the space of infinite sequences over the integers. Combinatorics in this setting is a powerful tool to understand the dynamics of transcendental maps and to understand the structure of specific families of transcendental maps. The study of combinatorics for transcendental maps is also likely to offer new insights in the combinatorics for rational maps and possibly in other areas of complex dynamical systems, like the systems generated by the iteration of holomorphic maps on manifolds with more than one complex dimension.

Оригинален текст от CORDIS (на английски).

Участници

UNIVERSITAT DE BARCELONA · BarcelonaКоординаторИспания