ergodic theorem 中文意思是什麼
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The most plausible operatorial generalization of result of preceding paragraph is known as the "mean ergodic theorem for unitary operators. "
前段結果可以推廣到運算元去，其中最近情近理的推廣是「單運算元的平均遍歷定理」。 -
We define a type of hyperbolicity on the full measure invariant set which is given by the oseledec ' s multiplicative ergodic theorem and prove that the system has the lipschitz shadowing property on it
對于由oseledec乘法遍歷定理得到的滿測度（ fullmeasure ）不變集定義了雙曲性，並證明了系統在這個不變集上具有lipschitz跟蹤性。 -
A necessary and sufficient condition with ergodic of 1 - order probability distribution function of stochastic process ( theorem 1 and corollary 1 ) and extended the general distribution theorem of stochastic variable under the case of weakly condition ( theorem2 ) are presented
摘要提出了隨機過程一階概率分佈函數具有遍歷性的一個充分必要條件（定理1和推論1 ） ，並在較弱條件下，對一般的關于隨機變量函數分佈定理作了進一步的推廣（定理2 ） 。 -
The most plausible operatorial generalization of result of preceding paragraph is known as the " mean ergodic theorem for unitary operators.
前段結果可以推廣到運算元去，其中最近情近理的推廣是「單運算元的平均遍歷定理」 。 -
Chapter 2 of this paper, by using a new method of proof, we obtain the weak ergodic convergence theorem for general semigroups of asymptotically nonexpansive type semigroups in reflexive banach space. by theorem 2. 1 of chapter 1 we get the weak ergodic convergence theorem of almost orbit for general semigroups of asymptotically nonexpansive type semigroups in reflexive banach space. by this method of proof, we give the weak ergodic convergence theorems for right reversible semigroups. by theorem 2. 1 of chapter l, we generalize the result to almost orbit case. so we can remove a key supposition that almost orbit is almost asymptotically isometric. it includes all commutative semigroups cases. baillon [ 8 ], hirano and takahashi [ 9 ] gave nonlinear retraction theorems for nonexpansive semigroups. recently mizoguchi and takahashi [ 10 ] proved a nonlinear ergodic retraction theorem for lipschitzian semigroups. hirano and kido and takahashi [ 11 ], hirano [ 12 ] gave nonlinear retraction theorems for nonexpansive mappings in uniformly convex banach spaces with frechet differentiable norm. in 1997, li and ma [ 16 ] proved the ergodic retraction theorem for general semitopological semigroups in hilbert space without the conditions that the domain is closed and convex, which greatly extended the fields of applications of ergodic theory. chapter 2 of this paper, we obtain the ergodic retraction theorem for general semigroups and almost orbits of asymptotically nonexpansive type semigroups in reflexive banach spaces. and we give the ergodic retraction theorem for almost orbits of right reversible semitopological semigroups
近年來， bruck [ 5 ] ， reich [ 6 ] ， oka [ 7 ]等在具frechet可微范數的一致凸banach空間中給出了非擴張及漸近非擴張映射及半群的遍歷收斂定理。 li和ma [ 13 ]在具frechet可微范數的自反banach空間中給出了一般交換漸近非擴張型拓撲半群的遍歷收斂定理，這是一個重大突破。本文第二章用一種新的證明方法在自反banach空間中，研究了揚州大學碩士學位論文2一般半群上的（ r ）類漸近非擴張型半群的弱遍歷收斂定理，即:定理3 . 1設x是具性質（ f ）的實自反banach空間， c是x的非空有界閉凸子集， g為含單位元的一般半群， s =仕工， 。 -
Reich [ 2 ] proved the ergodic theorems to nonexpansive semigroups in hilbert spaces. takahashi and zhang [ 3 ], tan and xu [ 4 ] extended baillon ' s theorem to asymptotically nonexpansive and asymptotically nonexpansive type semigroups in hilbert spaces. recently, reich [ 6 ], bruck [ 5 ], oka [ 7 ] gave the ergodic convergence theorems for nonexpansive, asymptotically nonexpansive mappings and semigroups in uniformly convex banach spaces with frechet differentiable norm. li and ma [ 13 ] obtained the ergodic convergence theorems for general commutative asymptotically nonexpansive type topological semigroups in reflexive banach space, which is a great breakthrough
Baillon [ 1 ]首先在hilbert空間的非空凸閉子集上給出了非擴張映照的弱遍歷收斂定理。 baillon的定理引起了很多數學家的興趣， reich [ 2 ]在hilbert空間中證明了非擴張半群的遍歷收斂定理。 takahashi和zhang [ 3 ] ， tan和xu [ 4 ]分別將baillon的定理推廣到漸近非擴張半群及漸近非擴張型半群。 -
Nonlinear operator theorem is now a focus in nonlinear theorem. the study of the ergodic theory for semitopologocal semigroups of nonlinear operators began in the middle of 1970 ' s. it got great development because it was widely used in many problems, such as the numerical solution of differentiable equation, the existence theory of positive solution, contral theory and optimization
非線性運算元理論是非線性理論中的熱門話題，它的研究始於上世紀七十年代中期，由於它被廣泛的應用於微分方程的數值解、正解的存在性理論、控制論以及最優化等問題中，因而得到了很大的發展。 -
( 2 ) as an application of ( 1 ), in view of the vagueness in the proof of the theorem 2. 1 : " a continuous flow is uniquely ergodic on 2 - dimensional torus if and only if it has at most one periodic orbit " in [ 2 ], we give it a proof
（ 2 ）作為（ 1 ）的應用，針對[ 2 ]的定理2 . 1 ： 「環面上無不動點的連續流是唯一遍歷的當且僅當它至多有一條周期軌」證明中所存在的含糊之處，我們給出了它的一個證明。 -
Some fundamental methods in mathematical analysis are applied to prove the unique decomposition theorem : the distance between vector - valued pseudo almost periodic functions in metric spaces and almost periodic functions is an ergodic perturbation
應用數學分析中的基本方法證明了唯一分解定理，即距離空間中的向量值偽概周期函數和概周期函數之間的距離是一個遍歷擾動。
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