- formulasearchengine

General

Display information for equation id:math.248967.23 on revision:248967

* Page found: Stable manifold (eq math.248967.23)

Occurrences on the following pages:

Stable manifold Eq: math.248967.23

Hash: cf3e145df16b9194325bbf3c65e5a149

TeX (original user input):

W^u_{\mathrm{loc}}(f,p,U) = W^s_{\mathrm{loc}}(f^{-1},p,U).

TeX (checked):

W_{\mathrm {loc} }^{u}(f,p,U)=W_{\mathrm {loc} }^{s}(f^{-1},p,U).

LaTeXML (experimental; uses MathML) rendering

MathML (5.932 KB / 1018 B) :

{\displaystyle W_{{{\mathrm{loc}}}}^{u}(f,p,U)=W_{{{\mathrm{loc}}}}^{s}(f^{{-1% }},p,U).}

<math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle W_{{{\mathrm{loc}}}}^{u}(f,p,U)=W_{{{\mathrm{loc}}}}^{s}(f^{{-1%&#10;}},p,U).}" display="inline">
  <semantics id="p1.1.m1.1a">
    <mrow id="p1.1.m1.1.24" xref="p1.1.m1.1.24.2.cmml">
      <mrow id="p1.1.m1.1.24.2" xref="p1.1.m1.1.24.2.cmml">
        <mrow id="p1.1.m1.1.24.2.1" xref="p1.1.m1.1.24.2.1.cmml">
          <msubsup id="p1.1.m1.1.24.2.1.2" xref="p1.1.m1.1.24.2.1.2.cmml">
            <mi id="p1.1.m1.1.1" xref="p1.1.m1.1.1.cmml">W</mi>
            <mi id="p1.1.m1.1.2.1" xref="p1.1.m1.1.2.1.cmml">loc</mi>
            <mi id="p1.1.m1.1.3.1" xref="p1.1.m1.1.3.1.cmml">u</mi>
          </msubsup>
          <mo id="p1.1.m1.1.24.2.1.1" xref="p1.1.m1.1.24.2.1.1.cmml">⁢</mo>
          <mrow id="p1.1.m1.1.24.2.1.3" xref="p1.1.m1.1.24.2.1.3.1.cmml">
            <mo stretchy="false" id="p1.1.m1.1.4" xref="p1.1.m1.1.24.2.1.3.1.cmml">(</mo>
            <mi id="p1.1.m1.1.5" xref="p1.1.m1.1.5.cmml">f</mi>
            <mo id="p1.1.m1.1.6" xref="p1.1.m1.1.24.2.1.3.1.cmml">,</mo>
            <mi id="p1.1.m1.1.7" xref="p1.1.m1.1.7.cmml">p</mi>
            <mo id="p1.1.m1.1.8" xref="p1.1.m1.1.24.2.1.3.1.cmml">,</mo>
            <mi id="p1.1.m1.1.9" xref="p1.1.m1.1.9.cmml">U</mi>
            <mo stretchy="false" id="p1.1.m1.1.10" xref="p1.1.m1.1.24.2.1.3.1.cmml">)</mo>
          </mrow>
        </mrow>
        <mo id="p1.1.m1.1.11" xref="p1.1.m1.1.11.cmml">=</mo>
        <mrow id="p1.1.m1.1.24.2.2" xref="p1.1.m1.1.24.2.2.cmml">
          <msubsup id="p1.1.m1.1.24.2.2.2" xref="p1.1.m1.1.24.2.2.2.cmml">
            <mi id="p1.1.m1.1.12" xref="p1.1.m1.1.12.cmml">W</mi>
            <mi id="p1.1.m1.1.13.1" xref="p1.1.m1.1.13.1.cmml">loc</mi>
            <mi id="p1.1.m1.1.14.1" xref="p1.1.m1.1.14.1.cmml">s</mi>
          </msubsup>
          <mo id="p1.1.m1.1.24.2.2.1" xref="p1.1.m1.1.24.2.2.1.cmml">⁢</mo>
          <mrow id="p1.1.m1.1.24.2.2.3" xref="p1.1.m1.1.24.2.2.3.1.cmml">
            <mo stretchy="false" id="p1.1.m1.1.15" xref="p1.1.m1.1.24.2.2.3.1.cmml">(</mo>
            <msup id="p1.1.m1.1.24.2.2.3.2" xref="p1.1.m1.1.24.2.2.3.2.cmml">
              <mi id="p1.1.m1.1.16" xref="p1.1.m1.1.16.cmml">f</mi>
              <mrow id="p1.1.m1.1.17.1" xref="p1.1.m1.1.17.1.cmml">
                <mo id="p1.1.m1.1.17.1.1" xref="p1.1.m1.1.17.1.1.cmml">-</mo>
                <mn id="p1.1.m1.1.17.1.2" xref="p1.1.m1.1.17.1.2.cmml">1</mn>
              </mrow>
            </msup>
            <mo id="p1.1.m1.1.18" xref="p1.1.m1.1.24.2.2.3.1.cmml">,</mo>
            <mi id="p1.1.m1.1.19" xref="p1.1.m1.1.19.cmml">p</mi>
            <mo id="p1.1.m1.1.20" xref="p1.1.m1.1.24.2.2.3.1.cmml">,</mo>
            <mi id="p1.1.m1.1.21" xref="p1.1.m1.1.21.cmml">U</mi>
            <mo stretchy="false" id="p1.1.m1.1.22" xref="p1.1.m1.1.24.2.2.3.1.cmml">)</mo>
          </mrow>
        </mrow>
      </mrow>
      <mo id="p1.1.m1.1.23" xref="p1.1.m1.1.24.2.cmml">.</mo>
    </mrow>
    <annotation-xml encoding="MathML-Content" id="p1.1.m1.1b">
      <apply id="p1.1.m1.1.24.2.cmml" xref="p1.1.m1.1.24">
        <eq id="p1.1.m1.1.11.cmml" xref="p1.1.m1.1.11"/>
        <apply id="p1.1.m1.1.24.2.1.cmml" xref="p1.1.m1.1.24.2.1">
          <times id="p1.1.m1.1.24.2.1.1.cmml" xref="p1.1.m1.1.24.2.1.1"/>
          <apply id="p1.1.m1.1.24.2.1.2.cmml" xref="p1.1.m1.1.24.2.1.2">
            <csymbol cd="ambiguous" id="p1.1.m1.1.24.2.1.2.1.cmml" xref="p1.1.m1.1.24.2.1.2">superscript</csymbol>
            <apply id="p1.1.m1.1.24.2.1.2.2.cmml" xref="p1.1.m1.1.24.2.1.2">
              <csymbol cd="ambiguous" id="p1.1.m1.1.24.2.1.2.2.1.cmml" xref="p1.1.m1.1.24.2.1.2">subscript</csymbol>
              <ci id="p1.1.m1.1.1.cmml" xref="p1.1.m1.1.1">𝑊</ci>
              <ci id="p1.1.m1.1.2.1.cmml" xref="p1.1.m1.1.2.1">loc</ci>
            </apply>
            <ci id="p1.1.m1.1.3.1.cmml" xref="p1.1.m1.1.3.1">𝑢</ci>
          </apply>
          <vector id="p1.1.m1.1.24.2.1.3.1.cmml" xref="p1.1.m1.1.24.2.1.3">
            <ci id="p1.1.m1.1.5.cmml" xref="p1.1.m1.1.5">𝑓</ci>
            <ci id="p1.1.m1.1.7.cmml" xref="p1.1.m1.1.7">𝑝</ci>
            <ci id="p1.1.m1.1.9.cmml" xref="p1.1.m1.1.9">𝑈</ci>
          </vector>
        </apply>
        <apply id="p1.1.m1.1.24.2.2.cmml" xref="p1.1.m1.1.24.2.2">
          <times id="p1.1.m1.1.24.2.2.1.cmml" xref="p1.1.m1.1.24.2.2.1"/>
          <apply id="p1.1.m1.1.24.2.2.2.cmml" xref="p1.1.m1.1.24.2.2.2">
            <csymbol cd="ambiguous" id="p1.1.m1.1.24.2.2.2.1.cmml" xref="p1.1.m1.1.24.2.2.2">superscript</csymbol>
            <apply id="p1.1.m1.1.24.2.2.2.2.cmml" xref="p1.1.m1.1.24.2.2.2">
              <csymbol cd="ambiguous" id="p1.1.m1.1.24.2.2.2.2.1.cmml" xref="p1.1.m1.1.24.2.2.2">subscript</csymbol>
              <ci id="p1.1.m1.1.12.cmml" xref="p1.1.m1.1.12">𝑊</ci>
              <ci id="p1.1.m1.1.13.1.cmml" xref="p1.1.m1.1.13.1">loc</ci>
            </apply>
            <ci id="p1.1.m1.1.14.1.cmml" xref="p1.1.m1.1.14.1">𝑠</ci>
          </apply>
          <vector id="p1.1.m1.1.24.2.2.3.1.cmml" xref="p1.1.m1.1.24.2.2.3">
            <apply id="p1.1.m1.1.24.2.2.3.2.cmml" xref="p1.1.m1.1.24.2.2.3.2">
              <csymbol cd="ambiguous" id="p1.1.m1.1.24.2.2.3.2.1.cmml" xref="p1.1.m1.1.24.2.2.3.2">superscript</csymbol>
              <ci id="p1.1.m1.1.16.cmml" xref="p1.1.m1.1.16">𝑓</ci>
              <apply id="p1.1.m1.1.17.1.cmml" xref="p1.1.m1.1.17.1">
                <minus id="p1.1.m1.1.17.1.1.cmml" xref="p1.1.m1.1.17.1.1"/>
                <cn type="integer" id="p1.1.m1.1.17.1.2.cmml" xref="p1.1.m1.1.17.1.2">1</cn>
              </apply>
            </apply>
            <ci id="p1.1.m1.1.19.cmml" xref="p1.1.m1.1.19">𝑝</ci>
            <ci id="p1.1.m1.1.21.cmml" xref="p1.1.m1.1.21">𝑈</ci>
          </vector>
        </apply>
      </apply>
    </annotation-xml>
    <annotation encoding="application/x-tex" id="p1.1.m1.1c">{\displaystyle W_{{{\mathrm{loc}}}}^{u}(f,p,U)=W_{{{\mathrm{loc}}}}^{s}(f^{{-1%
}},p,U).}</annotation>
  </semantics>
</math>

SVG (11.815 KB / 4.139 KB) :

SVG (MathML can be enabled via browser plugin) rendering

MathML (1.735 KB / 433 B) :

W_{\mathrm {loc} }^{u}(f,p,U)=W_{\mathrm {loc} }^{s}(f^{-1},p,U).

<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle W_{\mathrm {loc} }^{u}(f,p,U)=W_{\mathrm {loc} }^{s}(f^{-1},p,U).}">
  <semantics>
    <mrow class="MJX-TeXAtom-ORD">
      <mstyle displaystyle="true" scriptlevel="0">
        <msubsup>
          <mi>W</mi>
          <mrow class="MJX-TeXAtom-ORD">
            <mrow class="MJX-TeXAtom-ORD">
              <mi mathvariant="normal">l</mi>
              <mi mathvariant="normal">o</mi>
              <mi mathvariant="normal">c</mi>
            </mrow>
          </mrow>
          <mrow class="MJX-TeXAtom-ORD">
            <mi>u</mi>
          </mrow>
        </msubsup>
        <mo stretchy="false">(</mo>
        <mi>f</mi>
        <mo>,</mo>
        <mi>p</mi>
        <mo>,</mo>
        <mi>U</mi>
        <mo stretchy="false">)</mo>
        <mo>=</mo>
        <msubsup>
          <mi>W</mi>
          <mrow class="MJX-TeXAtom-ORD">
            <mrow class="MJX-TeXAtom-ORD">
              <mi mathvariant="normal">l</mi>
              <mi mathvariant="normal">o</mi>
              <mi mathvariant="normal">c</mi>
            </mrow>
          </mrow>
          <mrow class="MJX-TeXAtom-ORD">
            <mi>s</mi>
          </mrow>
        </msubsup>
        <mo stretchy="false">(</mo>
        <msup>
          <mi>f</mi>
          <mrow class="MJX-TeXAtom-ORD">
            <mo>&#x2212;<!-- − --></mo>
            <mn>1</mn>
          </mrow>
        </msup>
        <mo>,</mo>
        <mi>p</mi>
        <mo>,</mo>
        <mi>U</mi>
        <mo stretchy="false">)</mo>
        <mo>.</mo>
      </mstyle>
    </mrow>
    <annotation encoding="application/x-tex">{\displaystyle W_{\mathrm {loc} }^{u}(f,p,U)=W_{\mathrm {loc} }^{s}(f^{-1},p,U).}</annotation>
  </semantics>
</math>

SVG (9.532 KB / 3.833 KB) :

Translations to Computer Algebra Systems

Translation to Maple

In Maple:

Translation to Mathematica

In Mathematica:

Identifiers

$W$

$\mathrm {loc}$

$u$

$f$

$p$

$U$

$W$

$\mathrm {loc}$

$s$

$f$

$p$

$U$

MathML observations

0results

no statistics present please run the maintenance script ExtractFeatures.php

0 results

General

LaTeXML (experimental; uses MathML) rendering

SVG (MathML can be enabled via browser plugin) rendering

Translations to Computer Algebra Systems

Translation to Maple

Translation to Mathematica

Similar pages

Identifiers

MathML observations

Navigation menu

General

LaTeXML (experimental; uses MathML) rendering

SVG (MathML can be enabled via browser plugin) rendering

Translations to Computer Algebra Systems

Translation to Maple

Translation to Mathematica

Similar pages

Identifiers

MathML observations

Navigation menu

Search