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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 wikiPageLength "19058".
- Lie_point_symmetry wikiPageOutDegree "46".
- Lie_point_symmetry wikiPageRevisionID "706638226".
- Lie_point_symmetry wikiPageWikiLink Algebra.
- Lie_point_symmetry wikiPageWikiLink Algebraic_structure.
- Lie_point_symmetry wikiPageWikiLink Algebraic_variety.
- Lie_point_symmetry wikiPageWikiLink Bäcklund_transform.
- Lie_point_symmetry wikiPageWikiLink Canonical_transformation.
- Lie_point_symmetry wikiPageWikiLink Category:Lie_groups.
- Lie_point_symmetry wikiPageWikiLink Category:Symmetry.
- Lie_point_symmetry wikiPageWikiLink Contact_geometry.
- Lie_point_symmetry wikiPageWikiLink Continuous_symmetry.
- Lie_point_symmetry wikiPageWikiLink Differential_form.
- Lie_point_symmetry wikiPageWikiLink Discrete_symmetry.
- Lie_point_symmetry wikiPageWikiLink Dynamical_system.
- Lie_point_symmetry wikiPageWikiLink Emmy_Noether.
- Lie_point_symmetry wikiPageWikiLink Flow_(mathematics).
- Lie_point_symmetry wikiPageWikiLink Group_action.
- Lie_point_symmetry wikiPageWikiLink Infinitesimal_generator.
- Lie_point_symmetry wikiPageWikiLink Integrability_conditions_for_differential_systems.
- Lie_point_symmetry wikiPageWikiLink Invariant_(mathematics).
- Lie_point_symmetry wikiPageWikiLink Jacobian_matrix_and_determinant.
- Lie_point_symmetry wikiPageWikiLink Lie_algebra.
- Lie_point_symmetry wikiPageWikiLink Lie_bracket_of_vector_fields.
- Lie_point_symmetry wikiPageWikiLink Lie_group.
- Lie_point_symmetry wikiPageWikiLink Logistic_function.
- Lie_point_symmetry wikiPageWikiLink Manifold.
- Lie_point_symmetry wikiPageWikiLink Maple_(software).
- Lie_point_symmetry wikiPageWikiLink Moving_frame.
- Lie_point_symmetry wikiPageWikiLink Ordinary_differential_equation.
- Lie_point_symmetry wikiPageWikiLink Partial_differential_equation.
- Lie_point_symmetry wikiPageWikiLink Pierre_François_Verhulst.
- Lie_point_symmetry wikiPageWikiLink Product_rule.
- Lie_point_symmetry wikiPageWikiLink Reduction_(mathematics).
- Lie_point_symmetry wikiPageWikiLink Rotation.
- Lie_point_symmetry wikiPageWikiLink Scaling_(geometry).
- Lie_point_symmetry wikiPageWikiLink Smooth.
- Lie_point_symmetry wikiPageWikiLink Sophus_Lie.
- Lie_point_symmetry wikiPageWikiLink State_variable.
- Lie_point_symmetry wikiPageWikiLink Topological_group.
- Lie_point_symmetry wikiPageWikiLink Translations.
- Lie_point_symmetry wikiPageWikiLink Vector_field.
- Lie_point_symmetry wikiPageWikiLink Élie_Cartan.
- Lie_point_symmetry wikiPageWikiLinkText "Lie point symmetry".
- Lie_point_symmetry wikiPageUsesTemplate Template:Expand_section.
- Lie_point_symmetry wikiPageUsesTemplate Template:Lie_groups.
- Lie_point_symmetry wikiPageUsesTemplate Template:Reflist.
- Lie_point_symmetry subject Category:Lie_groups.
- Lie_point_symmetry subject Category:Symmetry.
- Lie_point_symmetry type Physic.
- Lie_point_symmetry type Technique.
- 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 Q6543828.
- Lie_point_symmetry sameAs m.0bh8mpw.
- Lie_point_symmetry sameAs Q6543828.
- Lie_point_symmetry wasDerivedFrom Lie_point_symmetry?oldid=706638226.
- Lie_point_symmetry isPrimaryTopicOf Lie_point_symmetry.