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- Movable_singularity abstract "In the theory of ordinary differential equations, a movable singularity is a point where the solution of the equation behaves badly and which is "movable" in the sense that its location depends on the initial conditions of the differential equation.Suppose we have an ordinary differential equation in the complex domain. Any given solution y(x) of this equation may well have singularities at various points (i.e. points at which it is not a regular holomorphic function, such as branch points, essential singularities or poles). A singular point is said to be movable if its location depends on the particular solution we have chosen, rather than being fixed by the equation itself.For example the equationhas solution for any constant c. This solution has a branchpoint at , and so the equation has a movable branchpoint (since it depends on the choice of the solution, i.e. the choice of the constant c).It is a basic feature of linear ordinary differential equations that singularities of solutions occur only at singularities of the equation, and so linear equations do not have movable singularities.When attempting to look for 'good' nonlinear differential equations it is this property of linear equations that one would like to see: asking for no movable singularities is often too stringent, instead one often asks for the so-called Painlevé property: 'any movable singularity should be a pole', first used by Sofia Kovalevskaya.".
- Movable_singularity thumbnail MovingSingularity.png?width=300.
- Movable_singularity wikiPageID "7664719".
- Movable_singularity wikiPageRevisionID "544576021".
- Movable_singularity hasPhotoCollection Movable_singularity.
- Movable_singularity subject Category:Complex_analysis.
- Movable_singularity subject Category:Ordinary_differential_equations.
- Movable_singularity type Abstraction100002137.
- Movable_singularity type Communication100033020.
- Movable_singularity type DifferentialEquation106670521.
- Movable_singularity type Equation106669864.
- Movable_singularity type MathematicalStatement106732169.
- Movable_singularity type Message106598915.
- Movable_singularity type OrdinaryDifferentialEquations.
- Movable_singularity type Statement106722453.
- Movable_singularity comment "In the theory of ordinary differential equations, a movable singularity is a point where the solution of the equation behaves badly and which is "movable" in the sense that its location depends on the initial conditions of the differential equation.Suppose we have an ordinary differential equation in the complex domain. Any given solution y(x) of this equation may well have singularities at various points (i.e.".
- Movable_singularity label "Movable singularity".
- Movable_singularity label "Подвижная особенность".
- Movable_singularity label "動く特異点".
- Movable_singularity sameAs 動く特異点.
- Movable_singularity sameAs m.026887j.
- Movable_singularity sameAs Q4367122.
- Movable_singularity sameAs Q4367122.
- Movable_singularity sameAs Movable_singularity.
- Movable_singularity wasDerivedFrom Movable_singularity?oldid=544576021.
- Movable_singularity depiction MovingSingularity.png.
- Movable_singularity isPrimaryTopicOf Movable_singularity.
