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Display information for equation id:math.1354.126 on revision:1354
* Page found: Dynamische Systeme und deterministisches Chaos (eq math.1354.126)
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Hash: 91ec5953cb61afac3caa66b163068b30
TeX (original user input):
\begin{align}
& A=\left( \begin{matrix}
-\sigma & \sigma & 0 \\
-z & -1 & r-x \\
y & x & -b \\
\end{matrix} \right) \\
& \Rightarrow \Lambda =trA=-\left( \sigma +1+b \right) \\
& \Rightarrow V(t)={{e}^{-\left( \sigma +1+b \right)t}}{{V}_{0}}-t->\infty \to 0 \\
\end{align}
TeX (checked):
{\begin{aligned}&A=\left({\begin{matrix}-\sigma &\sigma &0\\-z&-1&r-x\\y&x&-b\\\end{matrix}}\right)\\&\Rightarrow \Lambda =trA=-\left(\sigma +1+b\right)\\&\Rightarrow V(t)={{e}^{-\left(\sigma +1+b\right)t}}{{V}_{0}}-t->\infty \to 0\\\end{aligned}}
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MathML (1.938 KB / 502 B) :
<math class="mwe-math-element" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mrow data-mjx-texclass="ORD"><mtable columnalign="right left right left right left right left right left right left" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true" rowspacing="3pt"><mtr><mtd></mtd><mtd><mi>A</mi><mo>=</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mrow data-mjx-texclass="ORD"><mtable columnspacing="1em" rowspacing="4pt"><mtr><mtd><mo>−</mo><mi>σ</mi></mtd><mtd><mi>σ</mi></mtd><mtd><mn>0</mn></mtd></mtr><mtr><mtd><mo>−</mo><mi>z</mi></mtd><mtd><mo>−</mo><mn>1</mn></mtd><mtd><mi>r</mi><mo>−</mo><mi>x</mi></mtd></mtr><mtr><mtd><mi>y</mi></mtd><mtd><mi>x</mi></mtd><mtd><mo>−</mo><mi>b</mi></mtd></mtr><mtr><mtd></mtd></mtr></mtable></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow></mtd></mtr><mtr><mtd></mtd><mtd><mo>⇒</mo><mi mathvariant="normal">Λ</mi><mo>=</mo><mi>t</mi><mi>r</mi><mi>A</mi><mo>=</mo><mo>−</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>σ</mi><mo>+</mo><mn>1</mn><mo>+</mo><mi>b</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow></mtd></mtr><mtr><mtd></mtd><mtd><mo>⇒</mo><mi>V</mi><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo><mo>=</mo><msup><mi>e</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mo>−</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>σ</mi><mo>+</mo><mn>1</mn><mo>+</mo><mi>b</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow><mi>t</mi></mrow></mrow></msup><msub><mi>V</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub><mo>−</mo><mi>t</mi><mo>−</mo><mo>></mo><mi mathvariant="normal">∞</mi><mo accent="false">→</mo><mn>0</mn></mtd></mtr><mtr><mtd></mtd></mtr></mtable></mrow></mstyle></mrow></math>
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