Is there a proof for this limit cycle equilibrium

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Consider a system of differential equations where both are both continuous partial derivatives. Let's call them $F$ and $G$. Is there a proof suggesting that if there exists a solution that is a limit cycle of the system (call it $l(t)$), the system must then have an equilibrium solution?




differential-equations partial-derivative limit-cycles




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    Consider a system of differential equations where both are both continuous partial derivatives. Let's call them $F$ and $G$. Is there a proof suggesting that if there exists a solution that is a limit cycle of the system (call it $l(t)$), the system must then have an equilibrium solution?




    differential-equations partial-derivative limit-cycles




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      Consider a system of differential equations where both are both continuous partial derivatives. Let's call them $F$ and $G$. Is there a proof suggesting that if there exists a solution that is a limit cycle of the system (call it $l(t)$), the system must then have an equilibrium solution?




      differential-equations partial-derivative limit-cycles




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      Consider a system of differential equations where both are both continuous partial derivatives. Let's call them $F$ and $G$. Is there a proof suggesting that if there exists a solution that is a limit cycle of the system (call it $l(t)$), the system must then have an equilibrium solution?





      differential-equations partial-derivative limit-cycles





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          There is a theorem that a closed trajectory always encloses at least one equilibrium point. See e.g. Boyce and diPrima, theorem 9.7.1.






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          • I cannot access this document. Is there a note where I can see the theorem?
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          • Try this where it's theorem 7.5.1.
            – Robert Israel
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          There is a theorem that a closed trajectory always encloses at least one equilibrium point. See e.g. Boyce and diPrima, theorem 9.7.1.






          share|cite|improve this answer





















          • I cannot access this document. Is there a note where I can see the theorem?
            – FireMeUP
            yesterday










          • Try this where it's theorem 7.5.1.
            – Robert Israel
            yesterday














          up vote
          0
          down vote













          There is a theorem that a closed trajectory always encloses at least one equilibrium point. See e.g. Boyce and diPrima, theorem 9.7.1.






          share|cite|improve this answer





















          • I cannot access this document. Is there a note where I can see the theorem?
            – FireMeUP
            yesterday










          • Try this where it's theorem 7.5.1.
            – Robert Israel
            yesterday












          up vote
          0
          down vote










          up vote
          0
          down vote









          There is a theorem that a closed trajectory always encloses at least one equilibrium point. See e.g. Boyce and diPrima, theorem 9.7.1.






          share|cite|improve this answer













          There is a theorem that a closed trajectory always encloses at least one equilibrium point. See e.g. Boyce and diPrima, theorem 9.7.1.







          share|cite|improve this answer













          share|cite|improve this answer



          share|cite|improve this answer











          answered yesterday









          Robert Israel

          303k22199438




          303k22199438











          • I cannot access this document. Is there a note where I can see the theorem?
            – FireMeUP
            yesterday










          • Try this where it's theorem 7.5.1.
            – Robert Israel
            yesterday
















          • I cannot access this document. Is there a note where I can see the theorem?
            – FireMeUP
            yesterday










          • Try this where it's theorem 7.5.1.
            – Robert Israel
            yesterday















          I cannot access this document. Is there a note where I can see the theorem?
          – FireMeUP
          yesterday




          I cannot access this document. Is there a note where I can see the theorem?
          – FireMeUP
          yesterday












          Try this where it's theorem 7.5.1.
          – Robert Israel
          yesterday




          Try this where it's theorem 7.5.1.
          – Robert Israel
          yesterday












           

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