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Display information for equation id:math.1354.98 on revision:1354

* Page found: Dynamische Systeme und deterministisches Chaos (eq math.1354.98)

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\begin{align}
  & \delta \bar{x}:=\bar{x}-\bar{x}* \\ 
 & \delta \dot{\bar{x}}=A\delta \bar{x} \\ 
 & mit:\ \delta {{{\dot{x}}}_{i}}=\sum\limits_{k=1}^{2f}{{{\left( \frac{\partial {{F}_{i}}}{\partial {{x}_{k}}} \right)}_{x*}}\delta {{x}_{k}}=}\sum\limits_{k,j=1}^{2f}{\left( {{J}_{ij}}\frac{{{\partial }^{2}}H}{\partial {{x}_{k}}\partial {{x}_{j}}} \right)\delta {{x}_{k}}} \\ 
 & \sum\limits_{j=1}^{2f}{{}}\left( {{J}_{ij}}\frac{{{\partial }^{2}}H}{\partial {{x}_{k}}\partial {{x}_{j}}} \right)={{A}_{ik}} \\ 
\end{align}

TeX (checked):

{\begin{aligned}&\delta {\bar {x}}:={\bar {x}}-{\bar {x}}*\\&\delta {\dot {\bar {x}}}=A\delta {\bar {x}}\\&mit:\ \delta {{\dot {x}}_{i}}=\sum \limits _{k=1}^{2f}{{{\left({\frac {\partial {{F}_{i}}}{\partial {{x}_{k}}}}\right)}_{x*}}\delta {{x}_{k}}=}\sum \limits _{k,j=1}^{2f}{\left({{J}_{ij}}{\frac {{{\partial }^{2}}H}{\partial {{x}_{k}}\partial {{x}_{j}}}}\right)\delta {{x}_{k}}}\\&\sum \limits _{j=1}^{2f}{}\left({{J}_{ij}}{\frac {{{\partial }^{2}}H}{\partial {{x}_{k}}\partial {{x}_{j}}}}\right)={{A}_{ik}}\\\end{aligned}}

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\begin{aligned} δ \bar{x} : = \bar{x} - \bar{x} * \\ δ \dot{\bar{x}} = A δ \bar{x} \\ m i t : δ {\dot{x}}_{i} = \sum_{k = 1}^{2 f} {(\frac{\partial F_{i}}{\partial x_{k}})}_{x *} δ x_{k} = \sum_{k, j = 1}^{2 f} (J_{i j} \frac{\partial^{2} H}{\partial x_{k} \partial x_{j}}) δ x_{k} \\ \sum_{j = 1}^{2 f} (J_{i j} \frac{\partial^{2} H}{\partial x_{k} \partial x_{j}}) = A_{i k} \end{aligned}

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Identifiers

$δ$

$\bar{x}$

$\bar{x}$

$\bar{x}$

$δ$

$\dot{\bar{x}}$

$A$

$δ$

$\bar{x}$

$m$

$i$

$t$

$δ$

${\dot{x}}_{i}$

$k$

$f$

$F_{i}$

$x_{k}$

$x$

$δ$

$x_{k}$

$k$

$j$

$f$

$J_{i j}$

$H$

$x_{k}$

$x_{j}$

$δ$

$x_{k}$

$j$

$f$

$J_{i j}$

$H$

$x_{k}$

$x_{j}$

$A_{i k}$

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