【作者】 程传博；

【导师】 金渝光；

【作者基本信息】 重庆师范大学 ， 基础数学， 2012， 硕士

【摘要】 非线性科学已经成为当今基础科学研究的一个热点,其中非线性动力系统扮演着十分重要的角色.非线性描述了一种非直线关系的变化方式,并且这种方式在生活中比比皆是.比如位移、浓度和价格等随时间的变化情况;人口预测;计算机程序生成,乃至天文学、地质学、心理学和经济决策等方面.这些东西都可以抽象为迭代、迭代根和迭代方程问题.所以对这些问题的研究是非常必要和重要意义的.这几个问题不是彼此孤立,而是联系非常紧密的.迭代刻划了事物运动的重要环节和发展趋势.通过迭代,人们不但可以预测未来,而且也可以追溯过去,这就是人们关注的终极性和长期性状态.另一方面,人们同样关心事物发展的全过程,特别是各个环节之间的事,这就是迭代运算的逆运算—迭代根(或迭代方程)问题.通过这样的方法,人们可以连接和还原事物的过程.不仅于此,人们还希望进一步深入地了解和掌握与之相关的知识:有迭代和迭代根推广的迭代方程.我们将看到,迭代理论在现实生活中产生的重要作用.然而,由于迭代运算具有全局性和非线性的特点,过程就非常复杂,使得问题的解决起来困难重重.本文试图就几类特殊函数展开讨论,安排内容如下:第一章中介绍迭代、迭代根和迭代方程发展的现状以及本文研究的主要问题;第二章中给出了计算迭代的几种方法和几类特殊函数的迭代表达式;第三章和第四章分别给出了迭代根和迭代方程解的存在性;最后一章综述了本文的研究成果,然后分析了其中存在的问题和指出了以后努力的方向.更多还原

【Abstract】 Nonlinear science has become a hot topic of today’s basic science research, thenonlinear dynamical system plays a very important role in nonlinear description of anon-linear relationship between the changes, and in this way in life, Bibi aresuch as dis-placement, concentration and price changes over time; population projections; computerprogram to generate, and even astronomy, geology, psychology and economic dec i-sion-making. these things can be abstracted for the iteration, iterative roots and Die-gobehalf of the equation of the research on these issues is very necessary and importantsignificance.These are not isolated from each other, but are very closely linked. Iteration depictsan important part of the movement of things and the development trend. Iter ation, it cannot only predict the future, but also can be traced back to the past, this is the people’sattentionultimate and long-term status. the other hand, people are also co ncerned aboutthe whole process of development of things, especially between the var ious links, whichis the inverse operation of iteration-iteration of the root (or iterative equation).throughthis method, people can connect and restore things. does not stop there, people alsowant to further in-depth understanding and knowledge of related knowledge: iterativeand iterative root promotion iterative equation. we will seean important role in iterationtheory in real life.However, due to the iterative computation of global and nonlinear characteristics,the process is very complex, making the solution to the problem is fraught with difficul-ties. This paper attempts to discuss a few special functions, arranged as follows:Iteration, iterative roots and iterative development status of the equation as well asthe main problem of this study are described in the first chapter; given in Chapter II ofiterations of several methods and iterative expression of several types of special func-tions;chapters and Chapter IV gives the iterative root and iterative equations existence;the final chapter summarizes the research results of this article, and then analyzed theexisting problems and pointed out that the direction of the future efforts.更多还原