2018英特爾ISEF學(xué)科最佳作品摘要：數(shù)學(xué) Best of Category Abstract: MATHEMATICS

獲獎作品基本信息

年份	2018
學(xué)科	數(shù)學(xué) MATHEMATICS
學(xué)校	West Shore Junior/Senior High School
國家/州	FL，United States of America

獲獎作品名稱

A Fine Classification of Second Minimal Odd Orbits

獲獎作品摘要

This paper presents the solution to the open problem of the fine classification of second minimal odd periodic orbits of continuous endomorphisms on the real line. It is rigorously proven that second minimal odd orbits (of any length 2k+1, where k>2), either have a Stefan structure, like that of a minimal odd orbit, or have one of 4k-3 types, each characterized with its own cyclic permutation and directed graph of transitions, unique up to an inverse. The result is applied to the overarching problem of deriving a universal law of distribution for periodic windows within the chaotic regime of the bifurcation diagram of the one-parameter family of unimodal maps. This paper adds to the growing evidence that a universal pattern of distribution can be revealed by fixing the maximum number of appearances for periodic windows, and comparing the topological structures of iterative orbits to the topological structure of the P-Linearization of Cyclic Permutations.

By proving a fine classification of second minimal odd orbits, similar to the fine classification of minimal odd orbits by Stefan in 1977, this paper has a tremendous impact in the field of Chaos Theory, offering a deeper understanding of the universal nature of periodic orbits that appear in the iterative functions used in applied mathematical fields such as Population Dynamics, Weather Prediction, and Fluid Turbulence.

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高中生科研學(xué)術(shù)活動 英特爾 Intel ISEF 簡介

英特爾國際科學(xué)與工程大獎賽，簡稱 "ISEF"，由美國 Society for Science and the Public（科學(xué)和公共服務(wù)協(xié)會）主辦，英特爾公司冠名贊助，是全球規(guī)模最大、等級最高的中學(xué)生的科研科創(chuàng)賽事。ISEF 的學(xué)術(shù)活動學(xué)科包括了所有數(shù)學(xué)、自然科學(xué)、工程的全部領(lǐng)域和部分社會科學(xué)。ISEF 素有全球青少年科學(xué)學(xué)術(shù)活動的“世界杯”之美譽，旨在鼓勵學(xué)生團隊協(xié)作，開拓創(chuàng)新，長期專一深入地研究自己感興趣的課題。

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英特爾 ISEF 學(xué)術(shù)活動詳細介紹

英特爾 ISEF 全程指導(dǎo)方案

· 數(shù)學(xué) · 物理 · 化學(xué) · 生物 · 計算機 · 工程 ·

學(xué)科簡介：數(shù)學(xué) MATHEMATICS

The study of the measurement, properties, and relationships of quantities and sets, using numbers and symbols. The deductive study of numbers, geometry, and various abstract constructs, or structures.

Subcategories:

Algebra?(ALB):?The study of algebraic operations and/or relations and the structures which arise from them. An example is given by (systems of) equations which involve polynomial functions of one or more variables.

Analysis?(ANL):?The study of infinitesimal processes in mathematics, typically involving the concept of a limit. This begins with differential and integral calculus, for functions of one or several variables, and includes differential equations.

Combinatorics, Graph Theory, and Game Theory?(CGG):?The study of combinatorial structures in mathematics, such as finite sets, graphs, and games, often with a view toward classification and/or enumeration.

Geometry and Topology?(GEO):?The study of the shape, size, and other properties of figures and spaces. Includes such subjects as Euclidean geometry, non-Euclidean geometries (spherical, hyperbolic, Riemannian, Lorentzian), and knot theory (classification of knots in 3-space).

Number Theory?(NUM):?The study of the arithmetic properties of integers and related topics such as cryptography.

Probability and Statistics?(PRO):?Mathematical study of random phenomena and the study of statistical tools used to analyze and interpret data.

Other?(OTH):?Studies that cannot be assigned to one of the above subcategories. If the project involves multiple subcategories, the principal subcategory should be chosen instead of Other.