想問下咩叫Offer of Tenure - Associate Professor
tenure prof姐係點對哩d 一無所知
計劃進修PhD/Research討論區(27) The brain is wider than the sky
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睇咗老婆先生
睇咗老婆先生
想問下咩叫Offer of Tenure - Associate Professor
tenure prof姐係點
睇咗老婆先生
想問下咩叫Offer of Tenure - Associate Professor
tenure prof姐係點
associate都鐵飯碗
想問下咩叫Offer of Tenure - Associate Professor
tenure prof姐係點
associate都鐵飯碗
想問下咩叫Offer of Tenure - Associate Professor
tenure prof姐係點
associate都鐵飯碗
http://www.ams.org/journals/bull/2017-54-01/S0273-0979-2016-01552-7/S0273-0979-2016-01552-7.pdf
WHAT ARE LYAPUNOV EXPONENTS, AND WHY ARE THEY INTERESTING?
碌落少少已經唔覺得interesting
WHAT ARE LYAPUNOV EXPONENTS, AND WHY ARE THEY INTERESTING?
碌落少少已經唔覺得interesting
http://www.ams.org/journals/bull/2017-54-01/S0273-0979-2016-01552-7/S0273-0979-2016-01552-7.pdf
WHAT ARE LYAPUNOV EXPONENTS, AND WHY ARE THEY INTERESTING?
碌落少少已經唔覺得interesting
hea左兩日突然間又新post!
http://www.ams.org/journals/bull/2017-54-01/S0273-0979-2016-01552-7/S0273-0979-2016-01552-7.pdf
WHAT ARE LYAPUNOV EXPONENTS, AND WHY ARE THEY INTERESTING?
碌落少少已經唔覺得interesting
Oseledets's theorem好interesting
不過篇文真係寫得麻麻地
Lyapunov exponent大致上就係睇一個dynamical system平均嘅"expansion rate"有幾快
例如f(x)=2x mod 1,你當依個map係個dynamical system on circle嘅話，你會發現依個map會將啲嘢「放大」（例如將[0,1/2]變做[0,1]
但如果你睇g(x)=3x mod 1,應該唔難想像g expand得快過f
個rate可以話係取決於個slope有幾大，上面嘅例子個slope係constant,所以你可以好隨便咁講f嘅rate係2，g嘅rate係3
不過咁樣會唔夠好，因為dynamical system睇嘅唔單止係f,仲想睇f(f(...f(x))...)嘅behaviour,所以要睇嘅應該係f^n嘅slope
用上面嘅例子,f^n嘅slope係2^n,g^n嘅slope係3^n,依個sequence唔converge,但take完logarithm然後除以n就好好多，分別係log2同log3
但喺一般情況，個map個slope唔會係constant,但你仍然可以consider log|(h^n)'(x)|,你會發現用chain rule後會變咗 sum log|h'(h^i(x))|,如果h係ergodic依個sum除以n會converge to integrate log|h'| over the space,而依個數字就係Lyapunov exponent,話你知h平均expand得幾快
http://www.ams.org/journals/bull/2017-54-01/S0273-0979-2016-01552-7/S0273-0979-2016-01552-7.pdf
WHAT ARE LYAPUNOV EXPONENTS, AND WHY ARE THEY INTERESTING?
碌落少少已經唔覺得interesting
Oseledets's theorem好interesting
不過篇文真係寫得麻麻地
Lyapunov exponent大致上就係睇一個dynamical system平均嘅"expansion rate"有幾快
例如f(x)=2x mod 1,你當依個map係個dynamical system on circle嘅話，你會發現依個map會將啲嘢「放大」（例如將[0,1/2]變做[0,1]
但如果你睇g(x)=3x mod 1,應該唔難想像g expand得快過f
個rate可以話係取決於個slope有幾大，上面嘅例子個slope係constant,所以你可以好隨便咁講f嘅rate係2，g嘅rate係3
不過咁樣會唔夠好，因為dynamical system睇嘅唔單止係f,仲想睇f(f(...f(x))...)嘅behaviour,所以要睇嘅應該係f^n嘅slope
用上面嘅例子,f^n嘅slope係2^n,g^n嘅slope係3^n,依個sequence唔converge,但take完logarithm然後除以n就好好多，分別係log2同log3
但喺一般情況，個map個slope唔會係constant,但你仍然可以consider log|(h^n)'(x)|,你會發現用chain rule後會變咗 sum log|h'(h^i(x))|,如果h係ergodic依個sum除以n會converge to integrate log|h'| over the space,而依個數字就係Lyapunov exponent,話你知h平均expand得幾快