• <tr id="yyy80"></tr>
  • <sup id="yyy80"></sup>
  • <tfoot id="yyy80"><noscript id="yyy80"></noscript></tfoot>
  • 99热精品在线国产_美女午夜性视频免费_国产精品国产高清国产av_av欧美777_自拍偷自拍亚洲精品老妇_亚洲熟女精品中文字幕_www日本黄色视频网_国产精品野战在线观看 ?

    非緊集上錯誤函數(shù)下自由半群作用的拓?fù)鋲?/h1>
    2022-11-28 12:30:52郭鍇肖倩馬東魁
    關(guān)鍵詞:馬東華南理工大學(xué)廣州

    郭鍇,肖倩,馬東魁

    華南理工大學(xué)數(shù)學(xué)學(xué)院,廣東 廣州 510641

    Topological pressure,introduced by Ruelle[1]and Walters[2],is a core concept in dynamical system and ergodic theory,and plays an important role in the study of thermodynamic formalism. From the viewpoint of dimension theory,Pesin and Pitskel[3-4]studied the topological pressure of non-compact subsets by using carátheory structure(C-P structure),and proposed the topological pressure of non-compact sets in dynamical systems,which is the generalization of Bowen's[5]topological entropy defined by non-compact sets. As the physical process evolves,it is natural for the evolution process to produce changes or some errors in the orbit calculation.However,a self-adaptable system should decrease errors over time. This prompted Cheng,Zhao et al[6]to study the dynamical systems under a mistake function. They defined the pressure for asymptotically sub-additive potentials under a mistake function,and proved that the topological pressure under a mistake function is equivalent to the topological pressure without mistake function by using the ergodic theory. Later,Chen et al[7]gave the concepts of topological pressure with mistake function and showed that the topological pressure under a mistake function on any subset is the same as the classical Pesin pressure of the subset in dynamical systems. This means that the topological pressure under a mistake function in the dynamical system is adaptive,which generalizes the result in the additive case in[3].

    With the development of research on dynamical systems,the dynamical systems of group action has attracted people's attention. To study some questions,Xiao et al[8]gave the definitions of topological pressure and upper and lower capacity topological pressures of a free semigroup action by using C-P structure,and obtained some properties of them. Naturally,we wonder if the topological pressure of free semigroup actions has the similar result in[7]. In order to answer this question,in this paper we introduce the definitions of topological pressure of free semigroup actions under a mistake function and show the topological pressure of free semigroup actions under a mistake function is the same as the topological pressure of free semigroup actions defined by Xiao and Ma[8].

    Furthermore,Gr?ger et al[9]showed that the entropy of the whole system with Bowen metric is equal to the entropy with mean metric. As an application,we prove that the topological pressure of free semigroup actions defined by Bowen metric coincides with the topological pressure of free semigroup actions defined by mean metric on a non-compact subset.

    This paper is organized as follows. In section 1,we give some preliminaries. In section 2,we introduce two definitions of topological pressure of free semigroup actions under a mistake function and prove the main results. Finally,we give an application.

    1 Preliminaries

    1.1 Words and sequences

    Letdenote the set of all finite words of symbols 0,1,…,m-1. For anyw∈,the length ofw,denoted by|w|,is defined the digits of symbols inw. Obviously,with respect to the law of composition is a free semigroup withmgenerators. We writew′≤wif there exists a wordsuch thatw=Forw=i1…ik∈,denotewˉ=ik…i1.

    Denote by Σmthe set of all two-side infinite sequences of symbols 0,1,…,m-1,that is,

    1.2 Mistake function

    Let's recall the definition of the mistake function in[7],which is a little bit different from[6,10].

    Definition 1Givenε0>0,the functiong:N ×(0,ε0]→R is called a mistake function ifg(n,ε) ≤g(n+ 1,ε) for allε∈(0,ε0]andn∈N and

    For a mistake functiong,ifε>ε0,setg(n,ε) =g(n,ε0).

    1.3 Definition of topological pressure of free semigroup actions by using open covers

    Let(X,d) be a compact metric space andGbe the free semigroup generated byf0,f1,…,fm-1,wherefi(0 ≤i≤m- 1) is continuous transformations fromXto itself. Givenφ0,φ1,…,φm-1∈C(X,R), denote Φ ={φ0,φ1,…,φm-1}. For simplicity of notation, we writefwinstead offi1°fi2°… °fin, wherew=i1i2…in∈Obviously,fww′=fw fw′for anyw,. Forw=i1i2…in∈,denote

    Xiao and Ma[8]introduced the notion of topological pressure of free semigroup actions by C-P structure as follows:

    Considering a finite open coverUofX,write | U |= max{|U|:U∈U},and let

    for all U ∈GwandGwcoversZ(i.e. for any U ∈Gw,

    Let

    We can easily verify that the functionM(Z,α,Φ,U,N) is non-decreasing asNincreases.Therefore,the following limit exists

    There is a critical value ofαat whichm(Z,α,Φ,U) jumps from ∞to 0. Denote

    The topological pressure of a free semigroupGwith respect to Φ on the setZis

    1.4 Definition of topological pressure of free semigroup actions by using the center of Bowen ball

    First,recall the definitions of the Bowen metric and(w,δ)-Bowen ball.

    LetXbe a compact metric space with metricd,f0,f1,…,fm-1continuous transformations fromXto itself.Suppose that a free semigroupGwithmgeneratorsf0,f1,…,fm-1acts onX. Denote Φ ={φ0,φ1,…,φm-1},whereφ0,φ1,…,φm-1∈C(X,R). For eachw∈,a new metricdwonX(named Bowen metric)is given by

    Based on the work of Climenhaga in[11],Xiao and Ma[8]defined the topological pressure of free semigroup actions by using the center of Bowen ball. Now,let us recall the definition of topological pressure of free semigroup actions by the center of Bowen ball in[8].

    Let F denote the collection of Bowen ball,that is,

    Givenw∈,|w|=N∈N,Z?Xandα∈R,define

    Set

    It is easy to verify that the functionM′(Z,α,Φ,δ,N) is non-decreasing asNincreases.Therefore,there exists the limit

    Same as above,denote the critical value ofαby

    The topological pressure of a free semigroupGwith respect to Φ on the setZis

    2 Main results and example

    Based on [6-7],in this section,we first give two concepts of topological pressure of free semigroup actions under a mistake function by using open covers and the center of mistake Bowen ball respectively. In addition,we show that these two concepts are equivalent to the definitions of the topological pressure of free semigroup actions introduced by Xiao and Ma[8]. Finally,we give a notion of mean metric and show that the topological pressure of free semigroup actions under a mistake function defined by Bowen metric agrees with the topological pressure of free semigroup actions defined by mean metric.

    Letf0,f1,…,fm-1be the continuous transformations from compact metric space (X,d) to itself. DenoteGthe free semigroup withmgeneratorsf0,f1,…,fm-1acting onX. Givenφ0,φ1,…,φm-1∈C(X,R),denote Φ ={φ0,φ1,…,φm-1}.

    2.1 Definition of topological pressure of free semigroup actions under a mistake function by using open covers

    Considering a finite open coverUofX. For any string U ∈Sn+1(U),let

    We can easily verify that the functionM(Z,α,Φ,U,N,g) is non-decreasing asNincreases. This guarantees the existence of the following limit

    There exists a critical value of the parameterα,which we will denote byPZ(G,Φ,U,g),wherem(Z,α,Φ,U,g) jumps from ∞to 0,that is,

    The following theorem discusses the connection between the above definition and the topological pressure of free semigroup actions defined by using open covers.

    Theorem 1For any setZ?X,the following limit exists and equals to the topological pressure of a free semigroup actionG,that is,

    ProofWe use the analogous method as that of[3]. On the one hand,givenw=i1i2…iN∈,for any U ∈Sn+1(U),we denote the word that corresponds to U bywUsuch that,and corresponds to UgbywUgsuch thatwUg=wU,then we have

    Let

    and

    whereG′w={Ug:U ∈,wUg=wU},γis a function such that

    for allm(U) ≥N+ 1 andγ→0 as|U| →0.Moreover,we can get

    which implies

    Taking the limitN→∞yields

    Therefore,

    and as|U| →0,that is,β→0,γ→0,we obtain

    By the arbitrariness ofε,we have

    On the other hand,note thatwU=wUg,for any Ug∈(U),we can find

    strings U ∈Sm(U) such that

    whereτis the collection of such U.Using Stirling formula,there existsγ1>0 such that

    for allm(U) ≥N+ 1,andγ1→0 as |U| →0. Givenw∈with |w| =N,andε>0,there is?S g(U)coveringZsuch that

    which implies

    Take the limitN→∞and we get

    Therefore,

    and as ||U →0,that is,β→0,γ→0,γ1→0,we obtain

    Sinceε>0 is arbitrary,we have

    This completes the proof.

    The quantityPZ(G,Φ,g) is called the topological pressure of a free semigroupGunder a mistake functiongwith respect to Φ on the setZ.

    2.2 Definition of topological pressure of free semigroup actions under a mistake function by using the center of mistake Bowen balls

    Now,we introduce a definition of mistake Bowen ballBw(g;x,δ) for a givenw∈F+m.

    Fix a numberδ>0. Givenw∈F+mand a pointx∈X,the mistake Bowen ballBw(g;x,δ) centered atxwith radiusδand length ||

    w+ 1 associated to the mistake functiongis given by the following set,i.e.,

    It is obvious that the(w,δ)-Bowen ball is a subset ofBw(g;x,δ).

    Now,we describe another approach to redifine the topological pressure of a free semigroupGunder a mistake functiongby the center of mistake Bowen ball.Define the collection of subsets

    It is easy to verify that the functionM′(Z,α,Φ,δ,N,g) is non-decreasing asNincreases. This guarantees the existence of the limit

    There exists a critical value of the parameterα,which we will denote byP′Z(G,Φ,δ,g), wherem′(Z,α,Φ,δ,g) jumps from ∞to 0,namely,

    The following theorem proves that the two definitions of topological pressure of free semigroup actions under a mistake function are equivalent.

    Theorem 2For any setZ?X,the following limit exists and equals toPZ(G,Φ,g) defined by using open covers,that is,

    ProofOur proof is adapted from Climenhaga's elegament argument in[11]. On the one hand,givenδ>0,let

    and

    Note thatm(U) =m(Ug′)=|w′ |+ 1,then

    Moreover,we can get

    which implies

    Taking the limitN→∞yields

    This implies that

    Asδ→0,that is,ε(δ) →0,|U| →0,γ→0,we obtain

    It follows

    Hence

    This implies that

    Taking the limit asδ→0 gives

    It is obvious thatBw(g″;x,δ) ?Bw(2g″;x,δ),then we obtain

    which completes the proof.

    2.3 Example

    Let(X,d) be a compact metric space,f0,f1,…,fm-1continuous transformations fromXto itself. Similar to the definition of mean metric in[12],for anyx,y∈X,w∈F+m,we define a mean metric-dwonXas follows:

    Forx∈Xandδ>0,let

    In 2015,Gr?ger and J?ger[9]gave a definition of topological entropy of the whole system in mean metric by using separated sets,and proved that the topological entropy defined by mean metric is equivalent to the topological entropy defined by Bowen metric. Similar to the process of defining topological pressure of a free semigroupGin Section 1,we can also use the center of(x,δ) to define topological pressure on non-compact subsetZ,denoted by(G,Φ).

    Proposition 1For anyZ?X,we have

    Now,we chooseg(n,ε) =nε. It's clear that this function satisfies the definition of the mistake function.By the following lemma and Theorem 1,it is easy to obtain the above proposition,hence we omit the proof.

    Lemma 3For anyx∈X,w∈,andε>0,we have

    ProofFor anyy∈X,w∈,ifdw(x,y) <ε,then(x,y) <ε,so we have

    Set

    whereAw={w′:w′≤w}.Since

    Thus,we obtain

    Theny∈Bw(g;x,).Therefore,we have

    猜你喜歡
    馬東華南理工大學(xué)廣州
    捐 款
    躬耕(2023年1期)2023-03-07 01:03:25
    沒有叫停!廣州舊改,還在穩(wěn)步推進(jìn)……
    Multiple solutions and hysteresis in the flows driven by surface with antisymmetric velocity profile?
    117平、4房、7飄窗,光大來驚艷廣州了!
    9000萬平!超20家房企廝殺! 2020年上半年,廣州“舊改王”花落誰家?
    多彩廣州
    小讀者(2020年4期)2020-06-16 03:34:08
    本期作者
    世界建筑(2018年5期)2018-05-25 09:51:38
    馬東生 作品
    當(dāng)機(jī)器人遇上人工智能——記華南理工大學(xué)自動化科學(xué)與工程學(xué)院副教授張智軍
    焦唯、王琪斐美術(shù)作品

    18禁在线无遮挡免费观看视频| 亚洲美女视频黄频| 日日撸夜夜添| 美女cb高潮喷水在线观看| 欧美极品一区二区三区四区| 国产毛片在线视频| 久久精品人妻少妇| 国产成人福利小说| 亚洲欧美中文字幕日韩二区| 在线观看一区二区三区激情| 国产精品一区二区性色av| 我的女老师完整版在线观看| av卡一久久| 成人鲁丝片一二三区免费| 国产在线男女| 精品熟女少妇av免费看| xxx大片免费视频| 日韩欧美精品免费久久| 国产精品麻豆人妻色哟哟久久| 香蕉精品网在线| 国产成人午夜福利电影在线观看| av在线观看视频网站免费| 亚州av有码| 日韩欧美精品免费久久| 国产免费又黄又爽又色| 交换朋友夫妻互换小说| 免费av毛片视频| 一二三四中文在线观看免费高清| 别揉我奶头 嗯啊视频| www.av在线官网国产| 亚洲精品日韩av片在线观看| 女人十人毛片免费观看3o分钟| 色视频www国产| 午夜免费男女啪啪视频观看| 久久久午夜欧美精品| 爱豆传媒免费全集在线观看| 水蜜桃什么品种好| 欧美日本视频| 日本色播在线视频| 国产免费视频播放在线视频| 精品亚洲乱码少妇综合久久| 亚洲电影在线观看av| 久久99热这里只有精品18| 亚洲国产精品成人综合色| 香蕉精品网在线| 十八禁网站网址无遮挡 | 网址你懂的国产日韩在线| 亚洲精品日韩av片在线观看| 亚洲高清免费不卡视频| 国产 一区 欧美 日韩| 九九在线视频观看精品| 自拍欧美九色日韩亚洲蝌蚪91 | 日韩成人av中文字幕在线观看| 欧美3d第一页| 日韩国内少妇激情av| 国产精品无大码| 偷拍熟女少妇极品色| 麻豆乱淫一区二区| 国产精品人妻久久久久久| 国产黄色免费在线视频| 久久99热这里只频精品6学生| 女人十人毛片免费观看3o分钟| 欧美成人精品欧美一级黄| 国产伦在线观看视频一区| 街头女战士在线观看网站| 国产精品精品国产色婷婷| 国产精品国产三级国产专区5o| 久热这里只有精品99| 午夜福利在线观看免费完整高清在| 18禁裸乳无遮挡动漫免费视频 | 男女边摸边吃奶| 国国产精品蜜臀av免费| 欧美3d第一页| 大陆偷拍与自拍| 搡女人真爽免费视频火全软件| 极品少妇高潮喷水抽搐| 亚洲成色77777| 国产伦精品一区二区三区视频9| 色播亚洲综合网| av线在线观看网站| 纵有疾风起免费观看全集完整版| 久久综合国产亚洲精品| 国产欧美日韩一区二区三区在线 | 热99国产精品久久久久久7| 亚洲在线观看片| 午夜福利网站1000一区二区三区| 亚洲最大成人av| 青春草国产在线视频| 欧美日本视频| 黄片wwwwww| 毛片一级片免费看久久久久| 免费少妇av软件| 日韩欧美 国产精品| 国产男女内射视频| 国产人妻一区二区三区在| 成年女人在线观看亚洲视频 | 中文字幕亚洲精品专区| 成年版毛片免费区| 97超视频在线观看视频| 好男人在线观看高清免费视频| 国产片特级美女逼逼视频| 国产精品麻豆人妻色哟哟久久| 纵有疾风起免费观看全集完整版| 免费大片18禁| 女的被弄到高潮叫床怎么办| 亚洲av二区三区四区| 亚洲av.av天堂| 亚洲最大成人手机在线| 18+在线观看网站| 黄片无遮挡物在线观看| 女人十人毛片免费观看3o分钟| 丝瓜视频免费看黄片| 色网站视频免费| 国产精品国产三级国产av玫瑰| 免费观看的影片在线观看| 夜夜爽夜夜爽视频| 国产亚洲5aaaaa淫片| 午夜免费鲁丝| 久久久久久久国产电影| 99视频精品全部免费 在线| 97超视频在线观看视频| 久久99热6这里只有精品| 久久鲁丝午夜福利片| 国产精品秋霞免费鲁丝片| 18禁裸乳无遮挡免费网站照片| 99热这里只有是精品50| 中文欧美无线码| av国产精品久久久久影院| 久久精品国产亚洲av天美| 高清午夜精品一区二区三区| 激情五月婷婷亚洲| 如何舔出高潮| 欧美日韩综合久久久久久| 各种免费的搞黄视频| 国产 精品1| 老女人水多毛片| 伊人久久精品亚洲午夜| 亚洲国产精品专区欧美| 一二三四中文在线观看免费高清| 伊人久久国产一区二区| 精品少妇黑人巨大在线播放| 黑人高潮一二区| 亚洲欧美一区二区三区国产| 欧美人与善性xxx| 一区二区av电影网| 水蜜桃什么品种好| 成人亚洲精品一区在线观看 | 中国国产av一级| 国产v大片淫在线免费观看| 女人久久www免费人成看片| 丰满人妻一区二区三区视频av| 麻豆成人午夜福利视频| 国产精品人妻久久久久久| 日韩伦理黄色片| 一本久久精品| 亚洲,欧美,日韩| 视频区图区小说| 春色校园在线视频观看| 欧美变态另类bdsm刘玥| 99热网站在线观看| 国产亚洲一区二区精品| 午夜福利在线观看免费完整高清在| 欧美少妇被猛烈插入视频| 亚洲精品456在线播放app| 成人亚洲欧美一区二区av| 亚洲国产欧美在线一区| 91精品国产九色| 99精国产麻豆久久婷婷| 超碰av人人做人人爽久久| 内地一区二区视频在线| 中文字幕av成人在线电影| 久久久久久久精品精品| 国产一区有黄有色的免费视频| 91午夜精品亚洲一区二区三区| 久久精品久久精品一区二区三区| 国产伦精品一区二区三区四那| 亚洲熟女精品中文字幕| 成年人午夜在线观看视频| 国产毛片在线视频| 一级片'在线观看视频| 日本黄色片子视频| 肉色欧美久久久久久久蜜桃 | 黄色日韩在线| 国产高清国产精品国产三级 | 三级男女做爰猛烈吃奶摸视频| 午夜激情久久久久久久| 别揉我奶头 嗯啊视频| 国产爱豆传媒在线观看| 亚洲高清免费不卡视频| 伦精品一区二区三区| 99久久中文字幕三级久久日本| 国产精品99久久99久久久不卡 | 亚洲精品国产av成人精品| 国产成人午夜福利电影在线观看| 少妇人妻 视频| 老司机影院成人| 亚洲性久久影院| 菩萨蛮人人尽说江南好唐韦庄| 人妻少妇偷人精品九色| 高清视频免费观看一区二区| 国产真实伦视频高清在线观看| 国产成人a∨麻豆精品| 欧美极品一区二区三区四区| 在线天堂最新版资源| 99九九线精品视频在线观看视频| 日韩视频在线欧美| 久久久久精品久久久久真实原创| 成年免费大片在线观看| 日韩欧美 国产精品| 欧美激情在线99| 国产免费又黄又爽又色| 亚洲怡红院男人天堂| 国产精品99久久99久久久不卡 | 国产片特级美女逼逼视频| 亚洲欧美日韩东京热| 日韩三级伦理在线观看| 女的被弄到高潮叫床怎么办| 免费高清在线观看视频在线观看| 毛片一级片免费看久久久久| 亚洲性久久影院| 日韩三级伦理在线观看| 日本三级黄在线观看| 国产乱人视频| 美女cb高潮喷水在线观看| 国产精品99久久久久久久久| 色哟哟·www| 久久久久久久国产电影| 亚洲av中文av极速乱| 男人添女人高潮全过程视频| 久久久久久久久大av| 秋霞在线观看毛片| 国产免费一级a男人的天堂| 久久99热这里只频精品6学生| 男人添女人高潮全过程视频| 一级毛片 在线播放| 久久精品久久久久久久性| 永久网站在线| videossex国产| 18+在线观看网站| 中国三级夫妇交换| 如何舔出高潮| 男人舔奶头视频| 欧美日韩国产mv在线观看视频 | 亚洲欧美日韩无卡精品| 日韩 亚洲 欧美在线| 欧美激情久久久久久爽电影| 18禁在线播放成人免费| 午夜视频国产福利| 在线观看三级黄色| 新久久久久国产一级毛片| 欧美亚洲 丝袜 人妻 在线| 婷婷色综合www| 内射极品少妇av片p| 欧美精品国产亚洲| 最近最新中文字幕大全电影3| 国产午夜精品久久久久久一区二区三区| 国产精品熟女久久久久浪| 大香蕉久久网| 亚洲精品久久午夜乱码| 欧美日本视频| 欧美国产精品一级二级三级 | 国产v大片淫在线免费观看| av网站免费在线观看视频| 国产成人a∨麻豆精品| 日韩成人伦理影院| 国产av不卡久久| 直男gayav资源| 国产精品偷伦视频观看了| 2021少妇久久久久久久久久久| 大香蕉久久网| 啦啦啦中文免费视频观看日本| 18+在线观看网站| 国产精品久久久久久精品电影| 99热这里只有是精品在线观看| 国内精品美女久久久久久| 少妇猛男粗大的猛烈进出视频 | 亚洲高清免费不卡视频| 麻豆成人av视频| 国产成人精品婷婷| 免费少妇av软件| 九九久久精品国产亚洲av麻豆| 性色av一级| 人妻夜夜爽99麻豆av| 欧美xxxx黑人xx丫x性爽| 亚洲经典国产精华液单| 久久精品久久精品一区二区三区| 在线精品无人区一区二区三 | 99热6这里只有精品| 久久久久久久国产电影| 日本午夜av视频| 少妇熟女欧美另类| 日韩av在线免费看完整版不卡| 禁无遮挡网站| 大香蕉久久网| 亚洲,一卡二卡三卡| 亚洲人成网站在线观看播放| 国产黄a三级三级三级人| 国产日韩欧美亚洲二区| 99热网站在线观看| 国产乱人偷精品视频| 97人妻精品一区二区三区麻豆| 亚洲精品第二区| 午夜福利在线观看免费完整高清在| 天天躁日日操中文字幕| 91狼人影院| 有码 亚洲区| 国产色爽女视频免费观看| 亚洲美女视频黄频| 亚洲av不卡在线观看| 日产精品乱码卡一卡2卡三| 人妻少妇偷人精品九色| 午夜福利高清视频| 麻豆成人午夜福利视频| 成人毛片60女人毛片免费| 日韩欧美精品免费久久| 国产精品一区二区在线观看99| 色视频在线一区二区三区| 免费看不卡的av| 一级片'在线观看视频| 丝袜喷水一区| 亚洲av免费在线观看| 久久精品国产鲁丝片午夜精品| 日本色播在线视频| 国产精品伦人一区二区| 国产真实伦视频高清在线观看| 国产乱来视频区| 国产乱人视频| 午夜激情福利司机影院| 亚洲一区二区三区欧美精品 | 哪个播放器可以免费观看大片| 人妻系列 视频| 久久精品人妻少妇| 久久人人爽人人片av| 午夜福利高清视频| 97精品久久久久久久久久精品| 国产女主播在线喷水免费视频网站| 高清欧美精品videossex| 欧美日韩综合久久久久久| 毛片一级片免费看久久久久| 老司机影院毛片| 天天躁日日操中文字幕| 久久久久久久久久人人人人人人| 王馨瑶露胸无遮挡在线观看| 色网站视频免费| 亚洲婷婷狠狠爱综合网| 99视频精品全部免费 在线| 大片免费播放器 马上看| 国产精品.久久久| 国产高清有码在线观看视频| 伦理电影大哥的女人| 欧美日韩视频高清一区二区三区二| 熟女av电影| 在线观看国产h片| 午夜视频国产福利| 听说在线观看完整版免费高清| 久久久欧美国产精品| 有码 亚洲区| 日韩一区二区视频免费看| 五月玫瑰六月丁香| 欧美潮喷喷水| 欧美国产精品一级二级三级 | 久久午夜福利片| 内射极品少妇av片p| 一级毛片久久久久久久久女| 日韩,欧美,国产一区二区三区| 超碰av人人做人人爽久久| 人妻一区二区av| 一级二级三级毛片免费看| 亚洲国产精品999| 嫩草影院精品99| 另类亚洲欧美激情| 青春草亚洲视频在线观看| 久久亚洲国产成人精品v| 国产视频首页在线观看| 日韩成人伦理影院| 最近中文字幕高清免费大全6| 久久久久久久久久成人| 免费观看无遮挡的男女| 亚洲成人av在线免费| 美女内射精品一级片tv| 99精国产麻豆久久婷婷| 男人和女人高潮做爰伦理| 天堂中文最新版在线下载 | 国产白丝娇喘喷水9色精品| 亚洲欧美日韩卡通动漫| 欧美最新免费一区二区三区| 丰满少妇做爰视频| 在线看a的网站| 中文乱码字字幕精品一区二区三区| 纵有疾风起免费观看全集完整版| 99热6这里只有精品| 国产极品天堂在线| 久热久热在线精品观看| 国内揄拍国产精品人妻在线| 国产亚洲av片在线观看秒播厂| 国产精品一及| 精品视频人人做人人爽| 狂野欧美激情性xxxx在线观看| 欧美潮喷喷水| 99九九线精品视频在线观看视频| 看免费成人av毛片| 嫩草影院入口| 夜夜看夜夜爽夜夜摸| 亚洲四区av| 身体一侧抽搐| 99热6这里只有精品| av在线观看视频网站免费| 亚洲成人一二三区av| 日本色播在线视频| 精品亚洲乱码少妇综合久久| 中文精品一卡2卡3卡4更新| 真实男女啪啪啪动态图| 亚洲自偷自拍三级| 欧美变态另类bdsm刘玥| 黄色怎么调成土黄色| 亚洲欧美日韩东京热| 卡戴珊不雅视频在线播放| 亚洲色图av天堂| av国产久精品久网站免费入址| 99精国产麻豆久久婷婷| 亚洲欧美中文字幕日韩二区| 国产精品偷伦视频观看了| 美女视频免费永久观看网站| 少妇人妻 视频| 乱码一卡2卡4卡精品| 国产亚洲91精品色在线| 小蜜桃在线观看免费完整版高清| 免费大片18禁| 人人妻人人澡人人爽人人夜夜| 一级毛片我不卡| 国产精品久久久久久久电影| 日韩 亚洲 欧美在线| 国产精品福利在线免费观看| 欧美高清性xxxxhd video| 亚洲av男天堂| 人妻 亚洲 视频| 免费大片18禁| av福利片在线观看| 亚洲最大成人手机在线| 婷婷色麻豆天堂久久| 成人二区视频| 亚洲怡红院男人天堂| 国产一区有黄有色的免费视频| 有码 亚洲区| 中国美白少妇内射xxxbb| 久久97久久精品| 在线a可以看的网站| 久久久色成人| 日日啪夜夜撸| 中文字幕亚洲精品专区| 爱豆传媒免费全集在线观看| 久久久欧美国产精品| 免费观看性生交大片5| 亚洲成色77777| 日本欧美国产在线视频| 亚洲真实伦在线观看| 国产乱来视频区| freevideosex欧美| 国产爽快片一区二区三区| 亚洲一级一片aⅴ在线观看| 夜夜爽夜夜爽视频| 亚洲av电影在线观看一区二区三区 | 只有这里有精品99| 特大巨黑吊av在线直播| 日韩三级伦理在线观看| 中国美白少妇内射xxxbb| 卡戴珊不雅视频在线播放| 天堂中文最新版在线下载 | 欧美潮喷喷水| 午夜亚洲福利在线播放| 国产高清不卡午夜福利| 好男人在线观看高清免费视频| 国产极品天堂在线| 欧美成人午夜免费资源| 2018国产大陆天天弄谢| 精品少妇黑人巨大在线播放| 最近手机中文字幕大全| 国产极品天堂在线| 亚洲av在线观看美女高潮| 亚洲国产欧美在线一区| 国产伦在线观看视频一区| 美女内射精品一级片tv| 在线观看av片永久免费下载| 美女视频免费永久观看网站| 一本色道久久久久久精品综合| 国产午夜精品一二区理论片| 国产av国产精品国产| 日本免费在线观看一区| 麻豆乱淫一区二区| 精品一区二区免费观看| 国产欧美日韩精品一区二区| 日本av手机在线免费观看| 高清午夜精品一区二区三区| 人妻系列 视频| 一区二区av电影网| 人妻 亚洲 视频| 欧美性猛交╳xxx乱大交人| 看十八女毛片水多多多| 精品人妻熟女av久视频| 日韩伦理黄色片| 国产免费又黄又爽又色| 日韩成人av中文字幕在线观看| 美女脱内裤让男人舔精品视频| 日韩 亚洲 欧美在线| 看非洲黑人一级黄片| 亚洲在线观看片| 国产精品女同一区二区软件| 高清午夜精品一区二区三区| 麻豆精品久久久久久蜜桃| www.色视频.com| 少妇的逼水好多| 91精品伊人久久大香线蕉| 夜夜看夜夜爽夜夜摸| 麻豆精品久久久久久蜜桃| 久久久成人免费电影| 午夜视频国产福利| 六月丁香七月| 天天躁夜夜躁狠狠久久av| 欧美极品一区二区三区四区| 日本猛色少妇xxxxx猛交久久| 精品少妇黑人巨大在线播放| 日本欧美国产在线视频| 亚洲精品日韩av片在线观看| 国产色婷婷99| 天美传媒精品一区二区| 熟女电影av网| 啦啦啦啦在线视频资源| 91精品一卡2卡3卡4卡| 性插视频无遮挡在线免费观看| 国产爱豆传媒在线观看| 成年av动漫网址| 男女边吃奶边做爰视频| 国产精品一区二区三区四区免费观看| 亚洲国产精品成人久久小说| 精华霜和精华液先用哪个| 欧美97在线视频| 69人妻影院| 亚洲欧美一区二区三区黑人 | 国产人妻一区二区三区在| 3wmmmm亚洲av在线观看| 青春草视频在线免费观看| 亚洲av电影在线观看一区二区三区 | 国产黄频视频在线观看| 国产色爽女视频免费观看| 色哟哟·www| 欧美日本视频| 久久97久久精品| av在线蜜桃| 成人亚洲精品av一区二区| 高清av免费在线| 99久久九九国产精品国产免费| 精品人妻熟女av久视频| 亚洲国产av新网站| 亚洲欧美成人精品一区二区| 亚洲国产最新在线播放| 街头女战士在线观看网站| 国产成人a区在线观看| 免费观看性生交大片5| 交换朋友夫妻互换小说| 丝瓜视频免费看黄片| 久久ye,这里只有精品| 99视频精品全部免费 在线| 成年免费大片在线观看| 亚洲国产欧美在线一区| 国产毛片a区久久久久| 国产 精品1| 精品国产三级普通话版| 亚洲精华国产精华液的使用体验| 一区二区三区乱码不卡18| 免费看a级黄色片| 最近最新中文字幕大全电影3| 天美传媒精品一区二区| 亚洲av欧美aⅴ国产| 蜜桃久久精品国产亚洲av| 国产精品爽爽va在线观看网站| 高清午夜精品一区二区三区| 美女视频免费永久观看网站| 色哟哟·www| 成人亚洲欧美一区二区av| 美女高潮的动态| 亚洲av免费在线观看| 黄色配什么色好看| 国产精品一区www在线观看| 亚洲欧洲国产日韩| 久久久欧美国产精品| 高清欧美精品videossex| 欧美日韩精品成人综合77777| 成人午夜精彩视频在线观看| 亚洲va在线va天堂va国产| 97人妻精品一区二区三区麻豆| 久久这里有精品视频免费| 丰满少妇做爰视频| 日本色播在线视频| 成人午夜精彩视频在线观看| 久久久久九九精品影院| 亚洲精品成人久久久久久| 成人欧美大片| 最后的刺客免费高清国语| 亚洲欧美精品专区久久| 夜夜爽夜夜爽视频| 亚洲高清免费不卡视频| 91aial.com中文字幕在线观看| 大又大粗又爽又黄少妇毛片口| 在线观看免费高清a一片| 亚洲精品,欧美精品| 国产淫语在线视频| 久久午夜福利片| 少妇人妻一区二区三区视频| 男女无遮挡免费网站观看| 欧美成人一区二区免费高清观看| 精品人妻视频免费看| 成年女人在线观看亚洲视频 | 亚洲精品日韩在线中文字幕| 国产一区有黄有色的免费视频| 色播亚洲综合网|