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- Lie_point_symmetry abstract "Towards the end of the nineteenth century, Sophus Lie introduced the notion of Lie group in order to study the solutions of ordinary differential equations (ODEs). He showed the following main property: the order of an ordinary differential equation can be reduced by one if it is invariant under one-parameter Lie group of point transformations. This observation unified and extended the available integration techniques. Lie devoted the remainder of his mathematical career to developing these continuous groups that have now an impact on many areas of mathematically-based sciences. The applications of Lie groups to differential systems were mainly established by Lie and Emmy Noether, and then advocated by Élie Cartan.Roughly speaking, a Lie point symmetry of a system is a local group of transformations that maps every solution of the system to another solution of the same system. In other words, it maps the solution set of the system to itself. Elementary examples of Lie groups are translations, rotations and scalings.The Lie symmetry theory is a well-known subject. In it are discussed continuous symmetries opposed to, for example, discrete symmetries. The literature for this theory can be found, among other places, in these notes.".
- Lie_point_symmetry wikiPageID "26520106".
- Lie_point_symmetry wikiPageRevisionID "592188472".
- Lie_point_symmetry hasPhotoCollection Lie_point_symmetry.
- Lie_point_symmetry subject Category:Lie_groups.
- Lie_point_symmetry subject Category:Symmetry.
- Lie_point_symmetry type Abstraction100002137.
- Lie_point_symmetry type Group100031264.
- Lie_point_symmetry type LieGroups.
- Lie_point_symmetry comment "Towards the end of the nineteenth century, Sophus Lie introduced the notion of Lie group in order to study the solutions of ordinary differential equations (ODEs). He showed the following main property: the order of an ordinary differential equation can be reduced by one if it is invariant under one-parameter Lie group of point transformations. This observation unified and extended the available integration techniques.".
- Lie_point_symmetry label "Lie point symmetry".
- Lie_point_symmetry sameAs m.0bh8mpw.
- Lie_point_symmetry sameAs Q6543828.
- Lie_point_symmetry sameAs Q6543828.
- Lie_point_symmetry sameAs Lie_point_symmetry.
- Lie_point_symmetry wasDerivedFrom Lie_point_symmetry?oldid=592188472.
- Lie_point_symmetry isPrimaryTopicOf Lie_point_symmetry.