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Liouville-Arnold theorem

Liouville-Arnold theorem proper noun: in dynamical systems theory, a theorem stating that if, in a Hamiltonian dynamical system with n degrees of freedom, there are also known n first integrals of motion that are independent and in involution, then there exists a canonical transformation to action-angle coordinates in which the transformed Hamiltonian is dependent only upon the action coordinates and the angle coordinates evolve linearly in time. Thus the equations of motion for the system can be solved in quadratures if the canonical transform is explicitly known.

Proper noun

the Liouville-Arnold theorem

  1. In dynamical systems theory, a theorem stating that if, in a Hamiltonian dynamical system with n degrees of freedom, there are also known n first integrals of motion that are independent and in involution, then there exists a canonical transformation to action-angle coordinates in which the transformed Hamiltonian is dependent only upon the action coordinates and the angle coordinates evolve linearly in time. Thus the equations of motion for the system can be solved in quadratures if the canonical transform is explicitly known.

Origin of Liouville-Arnold theorem

Named after Joseph Liouville and Vladimir Arnold.

Questions about Liouville-Arnold theorem

What does Liouville-Arnold theorem mean?
Liouville-Arnold theorem means in dynamical systems theory, a theorem stating that if, in a Hamiltonian dynamical system with n degrees of freedom, there are also known n first integrals of motion that are independent and in involution, then there exists a canonical transformation to action-angle coordinates in which the transformed Hamiltonian is dependent only upon the action coordinates and the angle coordinates evolve linearly in time. Thus the equations of motion for the system can be solved in quadratures if the canonical transform is explicitly known.
What part of speech is Liouville-Arnold theorem?
Liouville-Arnold theorem is a proper noun.

Words near Liouville-Arnold theorem in the dictionary

  1. Lious
  2. Liouville
  3. Liouville number
  4. Liouville numbers
  5. Liouville's formula
  6. Liouville-Arnold theorem
  7. Liouying
  8. lioz
  9. lip
  10. lip balm
  11. lip balms

Source and license

Adapted from Wiktionary: Liouville-Arnold theorem (page history and authors). Text available under the Creative Commons Attribution-ShareAlike 4.0 license. Word.ws reformatted the entry and added links. Wiktionary data of 2026-09-02.

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