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Display information for equation id:math.1966.10 on revision:1966
* Page found: Der Satz von Liouville (eq math.1966.10)
(force rerendering)Occurrences on the following pages:
Hash: c5371a906d195889d8a33c84d0c1bae6
TeX (original user input):
\begin{align}
& {{\Phi }_{t,{{t}_{0}}}}({{{\bar{x}}}_{0}})={{{\bar{x}}}_{0}}+\bar{F}({{{\bar{x}}}_{0}},t)(t-{{t}_{0}})+O({{(t-{{t}_{0}})}^{2}}) \\
& \bar{F}({{{\bar{x}}}_{0}},t)=J{{{\bar{H}}}_{,x}}=\left( \begin{matrix}
\frac{\partial H}{\partial p} \\
-\frac{\partial H}{\partial q} \\
\end{matrix} \right) \\
\end{align}
TeX (checked):
{\begin{aligned}&{{\Phi }_{t,{{t}_{0}}}}({{\bar {x}}_{0}})={{\bar {x}}_{0}}+{\bar {F}}({{\bar {x}}_{0}},t)(t-{{t}_{0}})+O({{(t-{{t}_{0}})}^{2}})\\&{\bar {F}}({{\bar {x}}_{0}},t)=J{{\bar {H}}_{,x}}=\left({\begin{matrix}{\frac {\partial H}{\partial p}}\\-{\frac {\partial H}{\partial q}}\\\end{matrix}}\right)\\\end{aligned}}
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MathML (2.867 KB / 492 B) :
<math xmlns="http://www.w3.org/1998/Math/MathML" class="mwe-math-element mwe-math-element-inline"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mtable displaystyle="true"><mtr><mtd class="mwe-math-columnalign-r"></mtd><mtd class="mwe-math-columnalign-l"><msub><mi>Φ</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>t</mi><mo>,</mo><msub><mi>t</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub></mrow></mrow></msub><mo stretchy="false">(</mo><msub><mover><mi>x</mi><mo>¯</mo></mover><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub><mo stretchy="false">)</mo><mo stretchy="false">=</mo><msub><mover><mi>x</mi><mo>¯</mo></mover><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub><mo stretchy="false">+</mo><mover><mi>F</mi><mo>¯</mo></mover><mo stretchy="false">(</mo><msub><mover><mi>x</mi><mo>¯</mo></mover><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub><mo>,</mo><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">−</mo><msub><mi>t</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub><mo stretchy="false">)</mo><mo stretchy="false">+</mo><mi>O</mi><mo stretchy="false">(</mo><msup><mrow data-mjx-texclass="ORD"><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">−</mo><msub><mi>t</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub><mo stretchy="false">)</mo></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd><mtd class="mwe-math-columnalign-l"><mover><mi>F</mi><mo>¯</mo></mover><mo stretchy="false">(</mo><msub><mover><mi>x</mi><mo>¯</mo></mover><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub><mo>,</mo><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mi>J</mi><msub><mover><mi>H</mi><mo>¯</mo></mover><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mo>,</mo><mi>x</mi></mrow></mrow></msub><mo stretchy="false">=</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mrow data-mjx-texclass="ORD"><mo data-mjx-texclass="OPEN"></mo><mtable><mtr><mtd><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><mi>H</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><mi>p</mi></mrow></mrow></mfrac></mrow></mtd></mtr><mtr><mtd><mo stretchy="false">−</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><mi>H</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>∂</mi><mi>q</mi></mrow></mrow></mfrac></mrow></mtd></mtr></mtable><mo fence="true" stretchy="true" symmetric="true" data-mjx-texclass="CLOSE"></mo></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd></mtr></mtable></mstyle></mrow></math>
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