From d886fd756d3722ed3a36763a32184972f84101e8 Mon Sep 17 00:00:00 2001 From: Petr Velycko Date: Thu, 15 May 2025 15:59:57 +0200 Subject: [PATCH] jeste lepsi dukaz --- floquetova-teorie.tex | 2 +- skripta.pdf | Bin 226869 -> 226907 bytes 2 files changed, 1 insertion(+), 1 deletion(-) diff --git a/floquetova-teorie.tex b/floquetova-teorie.tex index 4d2f8e8..774a659 100644 --- a/floquetova-teorie.tex +++ b/floquetova-teorie.tex @@ -75,7 +75,7 @@ Matici $C^k$ můžeme relativně snadno spočítat pomocí převodu na Jordanův \end{theorem} \begin{proof} - (ii) $\Leftrightarrow$ (iii): $x$ je $T$-periodické řešení právě tehdy když $x(T) = x(0)$, coz nastane právě tehdy když $Cx_0 = x_0$. + (ii) $\iff$ (iii): $x$ je netriviální $T$-periodické řešení právě tehdy, když $x(T) = x(0)$, coz nastane právě tehdy, když $Cx_0 = x_0$, tedy $1$ je vlastní číslo matice $C$. (i) $\implies$ (ii): Předpokládejme, že $x$ je $T$-periodické řešení \eqref{eq-linear-periodic} a pro spor předpokládejme, že $y$ je netriviální $T$-periodické řešení homogenní rovnice, tedy $x + y$ je $T$-periodické řešení \eqref{eq-linear-periodic}, ale $x + y \neq x$, což je spor s jednoznačností řešení nehomogenní úlohy. diff --git a/skripta.pdf b/skripta.pdf index 5617d759b024b407b8b6da81d818376354647745..9f54542800e23be021268c83cb843544d8705a62 100644 GIT binary patch delta 21518 zcmV)DK*7JY>YorDG=2TCO`(RyJ0pdD9U;~Zw(7(Mi#mnY(-XKLSC6LhJ035$(xsH&lrOWAwoQzft0m2#4>}+Y{7p7fkGowO=!}DAoMce zCp0#AH#*ROigWT zK8`1+qNiX&W;uu!-HDU~OD+xlQyFTTp+-eC!4>Z0jgO~vyg28|d;c_K;;5`=mN=cO z_ugibrqkTcBy)eDP9mFl)bZ)!<8l}n!g|I%MJ@5~VHKxumW811R%<*zak7ehV3IZ` z)NbqyiggnS3o#F3Fzpew3Idcy-ENT8#Auy7Gy;XA5bf@q5)2MWe8mmwL=k%YaFBfIdohsK7Bm{&8YHYS=fFIesTN-WQ|g@}@5XP!+86&I!YxJY{bJE`70x+vt9 z<%_z1EV@|huuSXOvRSuc1vUc;*b2v%_!(g2*&k)1tbIh&Wb=9~N2GYzO42VUrk$l% 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