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閲嶉粸(di菐n)鎺屾彙浜岀董鑷不绯荤当(t菕ng)鍒濈瓑濂囬粸(di菐n)鐨勫垎椤炲強鍏堕檮杩戠殑杌岀窔鍒嗗竷锛涚悊瑙g┅(w臎n)瀹氭€ф蹇靛強鍏跺垽瀹� 瀹氱悊锛屾渻(hu矛)鎳�(y墨ng)鐢ㄧ┅(w臎n)瀹氭€ф蹇�銆佺窔鎬у寲绯荤当(t菕ng)鐨勭壒寰佸€笺€丩iapunov 绗簩鏂规硶瑷庤珫鑷不绯荤当(t菕ng)鐨勮В鐨� 绌�(w臎n)瀹氭€�銆� 浜�銆� 鍙冭€冩浉鐩� 1銆� 鏉卞寳甯寖澶у(xu茅)鏁�(sh霉)瀛�(xu茅)绯�锛屻€婂父寰垎鏂圭▼銆嬶紝楂樼瓑鏁欒偛鍑虹増绀�锛�1982 骞淬€� 2銆� 钁夊毚(y谩n)璎�锛屻€婂父寰垎鏂圭▼銆�锛岄珮绛夋暀鑲插嚭鐗堢ぞ锛�1982 骞达紙绗簩鐗堬級銆� 3銆� 涓北澶у(xu茅)鏁�(sh霉)瀛�(xu茅)绯�锛屻€婂父寰垎鏂圭▼銆嬶紝楂樼瓑鏁欒偛鍑虹増绀�锛�1983 骞达紙绗簩鐗堬級銆� 4銆� 鍦嬪鏁欒偛濮斿摗鏈�(hu矛)甯寖鏁欒偛鍙革紝銆婃櫘閫氶珮搴﹀斧鑼冨(xu茅)鏍℃暩(sh霉)瀛�(xu茅)鏁欒偛灏堟キ(y猫)锛堟湰绉戯級鏁欒偛鏁欏(xu茅)鍩烘湰 瑕佹眰锛堣│琛岋級銆�锛岄閮藉斧鑼冨ぇ瀛�(xu茅)鍑虹増绀撅紝1994銆� 娉涘嚱鍒嗘瀽 绗竴绔� 搴﹂噺绌洪枔鑸囩窔鎬ц肠鑼冪┖闁� 鑰冭│瑕侀粸(di菐n)锛� 搴﹂噺绌洪枔鐨勬蹇�锛屼緥瀛�锛涘害閲忕┖闁撲腑鐨勬敹鏂傛€ц垏閫g簩(x霉)鎬�锛涚瀵嗘€�锛涘彲鍒嗘€�锛汣auchy 鍒� 鑸囧害閲忕┖闁撶殑瀹屽倷鎬�锛涘绺槧鍍忓師鐞嗗強鍏舵噳(y墨ng)鐢紱绶氭€ц肠鑼冪┖闁撶殑姒傚康锛屼緥瀛愶紱Banach 绌洪枔 鐨勬蹇�銆� 鑰冭│鍏�(n猫i)瀹癸細 绗竴绡€(ji茅) 搴﹂噺绌洪枔鐨勬蹇佃垏渚嬪瓙 璺濋洟鍙婂害閲忕┖闁撶殑瀹氱京锛涗緥瀛愶紙姝愭皬绌洪枔 n R 锛涢€g簩(x霉)鍑芥暩(sh霉)绌洪枔 ],[ baC 锛涙暩(sh霉)鍒楃┖闁� p l 绛夛級銆� 绗簩绡€(ji茅) 搴﹂噺绌洪枔涓殑妤甸檺? 绋犲瘑鎬�? 鍙垎绌洪枔 闋�(l菒ng)鍩熺殑姒傚康锛涙敹鏂傞粸(di菐n)鍒�锛涙湁鐣岄泦锛涘叿楂旂┖闁撲腑鏀舵杺鎬х殑鎰忕京锛涚瀵嗘€ц垏鍙垎绌洪枔鐨勬蹇�锛� 涓嶅彲鍒嗙┖闁撶殑渚嬪瓙銆� 绗笁绡€(ji茅) 閫g簩(x霉)鏄犲皠 鏄犲皠閫g簩(x霉)鎬х殑鍚勭ó瀹氱京鍙婂叾绛夊児(ji脿)鎬�銆� 绗洓绡€(ji茅) Cauchy 榛�(di菐n)鍒楄垏瀹屽倷搴﹂噺绌洪枔 搴﹂噺绌洪枔涓� Cauchy 榛�(di菐n)鍒楃殑姒傚康锛涘畬鍌欏害閲忕┖闁撶殑瀹氱京锛涘畬鍌欏害閲忕┖闁撹垏涓嶅畬鍌欏害閲忕┖ 闁撶殑鍚勯渚嬪瓙锛涘害閲忕┖闁撻枆瀛愮┖闁撶殑瀹屽倷鎬�銆� 绗簲绡€(ji茅) 搴﹂噺绌洪枔鐨勫畬鍌欏寲 绛夎窛鍚屾(g貌u)锛涘害閲忕┖闁撶殑瀹屽倷鍖栧畾鐞�锛� 绗叚绡€(ji茅) 澹撶府鏄犲儚鍘熺悊鍙婂叾鎳�(y墨ng)鐢� 澹撶府鏄犲儚鐨勫畾缇╋紱澹撶府鏄犲儚鍘熺悊锛涘湪闅卞嚱鏁�(sh霉)瀹氱悊鍙婂父寰垎鏂圭▼涓殑鎳�(y墨ng)鐢�銆� 绗竷绡€(ji茅) 绶氭€х┖闁� 鏈瘈(ji茅)鍏�(n猫i)瀹圭偤绶氭€х┖闁撶殑鍩烘湰姒傚康銆傚洜?q奴)W鐢熷凡鍦ㄩ珮绛変唬鏁�(sh霉)瑾茬▼涓(xu茅)閬庢湁闄愮董绌洪枔鐨勬湁闂�(gu膩n) 鍏�(n猫i)瀹�锛屾晠鍙渶绨�(ji菐n)瑕佸洖椤у苟寮�(qi谩ng)瑾�(di脿o)鐒¢檺缍窔鎬х┖闁撶殑鐗瑰緛鍗冲彲銆� 绗叓绡€(ji茅) 绶氭€ц肠鑼冪┖闁撳拰 Banach 绌洪枔 鑼冩暩(sh霉)锛岀窔鎬ц肠鑼冪┖闁撳拰 Banach 绌洪枔鐨勬蹇碉紱渚濊寖鏁�(sh霉)鏀舵杺锛� n R 绌洪枔锛� ],[ baC 绌洪枔锛� ? l 绌洪枔锛� ? 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