Wiki143:WikiProject Mathematics/PlanetMath Exchange/34-XX Ordinary differential equations

34-00 General reference works (handbooks, dictionaries, bibliographies, etc.)

• PM: contact point, id=5507 -- WP guess: contact point -- Status:

• PM: dependence on initial conditions of solutions of ordinary differential equations, id=4257 -- WP guess: dependence on initial conditions of solutions of ordinary differential equations -- Status:

• PM: differential equation, id=2969 -- WP guess: differential equation -- Status:

• PM: dynamical system, id=5508 -- WP: dynamical system -- Status: A

linas 00:18, 8 June 2006 (UTC)

• PM: existence and uniqueness of solution of ordinary differential equations, id=4246 -- WP guess: existence and uniqueness of solution of ordinary differential equations -- Status:

• PM: FitzHugh-Nagumo equation, id=6031 -- WP guess: FitzHugh-Nagumo equation -- Status:

• PM: Liapunov function, id=4386 -- WP: Lyapunov function -- Status: M

Copied by Rich Farmbrough to Liapunov function later merged by Blotwell into Lyapunov function. Paul August ☎ 21:25, 20 July 2007 (UTC)

• PM: Lorenz equation, id=4383 -- WP guess: Lorenz equation -- Status:

• PM: maximal interval of existence of ordinary differential equations, id=4251 -- WP guess: maximal interval of existence of ordinary differential equations -- Status:

• PM: method of undetermined coefficients, id=3224 -- WP: method of undetermined coefficients -- Status: A

Oleg Alexandrov 19:24, 13 August 2005 (UTC)

• PM: natural symmetry of the Lorenz equation, id=4428 -- WP guess: natural symmetry of the Lorenz equation -- Status:

• PM: rectification theorem, id=6649 -- WP guess: rectification theorem -- Status:

Before processing this, be sure to check http://planetmath.org/?op=getmsg&id=6042 CryptoDerk 16:59, Feb 3, 2005 (UTC)

• PM: separating solution, id=5505 -- WP guess: separating solution -- Status:

• PM: some qualitative analysis of FitzHugh-Nagumo equation using nullclines, id=6079 -- WP guess: some qualitative analysis of FitzHugh-Nagumo equation using nullclines -- Status:

• PM: symmetry of a solution of an ordinary differential equation, id=4385 -- WP guess: symmetry of a solution of an ordinary differential equation -- Status:

• PM: symmetry of an ordinary differential equation, id=4384 -- WP guess: symmetry of an ordinary differential equation -- Status:

• PM: Wronskian determinant, id=2164 -- WP: Wronskian determinant -- Status: C

Oleg Alexandrov 19:49, 13 August 2005 (UTC)

• PM: all solution of the Lorenz equation enter an ellipsoid, id=7042 -- WP guess: all solution of the Lorenz equation enter an ellipsoid -- Status:

• PM: bibliography for ordinary differential equations, id=7122 -- WP guess: bibliography for ordinary differential equations -- Status:

• PM: Index of differential equations, id=7023 -- WP guess: Index of differential equations -- Status:

• PM: Leibniz notation for vector fields, id=7296 -- WP guess: Leibniz notation for vector fields -- Status:

• PM: Lienard system, id=7166 -- WP guess: Lienard system -- Status:

• PM: linear ordinary differential equation, id=7389 -- WP guess: linear ordinary differential equation -- Status:

• PM: method of integrating factors, id=8710^new! -- WP guess: method of integrating factors -- Status:

• PM: stochastic differential equation, id=8252^new! -- WP guess: stochastic differential equation -- Status:

• PM: van der Pol equation, id=8177^new! -- WP guess: van der Pol equation -- Status:

34-01 Instructional exposition (textbooks, tutorial papers, etc.)

• PM: second order linear differential equation with constant coefficients, id=3960 -- WP guess: second order linear differential equation with constant coefficients -- Status:

• PM: harmonic oscillator, id=9745^new! -- WP guess: harmonic oscillator -- Status:

34A05 Explicit solutions and reductions

• PM: d'Alembert's equation, id=6058 -- WP guess: d'Alembert's equation -- Status:

• PM: separation of variables, id=2712 -- WP guess: separation of variables -- Status:

• PM: variation of parameters, id=2921 -- WP guess: variation of parameters -- Status:

• PM: solutions of ordinary differential equation, id=8719^new! -- WP guess: solutions of ordinary differential equation -- Status:

34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions

• PM: Cauchy initial value problem, id=6650 -- WP guess: Cauchy initial value problem -- Status:

• PM: initial value problem, id=5410 -- WP guess: initial value problem -- Status:

• PM: cycle, id=6721 -- WP guess: cycle -- Status:

• PM: limit cycle, id=6722 -- WP: limit cycle -- Status: A

linas 00:12, 8 June 2006 (UTC)

• PM: Peano's theorem, id=7157 -- WP guess: Peano's theorem -- Status:

• PM: Picard's theorem, id=6706 -- WP guess: Picard's theorem -- Status:

• PM: existence and uniqueness of solution to Cauchy problem, id=9173^new! -- WP guess: existence and uniqueness of solution to Cauchy problem -- Status:

34A25 Analytical theory: series, transformations, transforms, operational calculus, etc.

• PM: Fuchsian differential equation, id=6443 -- WP guess: Fuchsian differential equation -- Status:

• PM: Fuchsian singularity, id=6442 -- WP guess: Fuchsian singularity -- Status:

34A30 Linear equations and systems, general

• PM: Chebyshev equation, id=3616 -- WP guess: Chebyshev equation -- Status:

• PM: Green's function for differential operator, id=6356 -- WP guess: Green's function for differential operator -- Status:

• PM: example of solving a functional equation, id=7359 -- WP guess: example of solving a functional equation -- Status:

• PM: linear differential equation of first order, id=8717^new! -- WP guess: linear differential equation of first order -- Status:

34A34 Nonlinear equations and systems, general

• PM: gradient system, id=7014 -- WP guess: gradient system -- Status:

• PM: Liouville's theorem, id=7027 -- WP guess: Liouville's theorem -- Status:

34A99 Miscellaneous

• PM: autonomous system, id=4260 -- WP guess: autonomous system -- Status:

34B24 Sturm-Liouville theory

• PM: eigenfunction, id=3117 -- WP guess: eigenfunction -- Status:

34C05 Location of integral curves, singular points, limit cycles

• PM: Hopf bifurcation theorem, id=3819 -- WP guess: Hopf bifurcation theorem -- Status:

• PM: omega limit set, id=3818 -- WP: limit set -- Status: A

linas 15:54, 9 June 2006 (UTC)

• PM: orthogonal curves, id=6504 -- WP guess: orthogonal curves -- Status:

• PM: Poincare-Bendixson theorem, id=3817 -- WP guess: Poincare-Bendixson theorem -- Status:

• PM: Bernoulli equation, id=7032 -- WP guess: Bernoulli equation -- Status:

• PM: Clairaut's equation, id=7024 -- WP guess: Clairaut's equation -- Status:

34C07 Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramif

• PM: Bamòn's theorem, id=6002 -- WP guess: Bamòn's theorem -- Status:

• PM: Bautin's theorem, id=6011 -- WP guess: Bautin's theorem -- Status:

• PM: Dulac's theorem, id=5930 -- WP guess: Dulac's theorem -- Status:

• PM: Hilbert's 16th problem for quadratic vector fields, id=5415 -- WP guess: Hilbert's 16th problem for quadratic vector fields -- Status:

34C08 Connections with real algebraic geometry (fewnomials, desingularization, zeros of Abelian integrals, etc.)

• PM: Rolle's theorem for dynamical systems in the plane, id=5514 -- WP guess: Rolle's theorem for dynamical systems in the plane -- Status:

34C23 Bifurcation

• PM: bifurcation, id=2821 -- WP: Bifurcation theory -- Status: A

Jeekc 10:52, 15 December 2005 (UTC)

34C25 Periodic solutions

• PM: Bendixson's negative criterion, id=4103 -- WP guess: Bendixson's negative criterion -- Status:

• PM: Dulac's criteria, id=4252 -- WP guess: Dulac's criteria -- Status:

• PM: proof of Bendixson's negative criterion, id=4105 -- WP guess: proof of Bendixson's negative criterion -- Status:

34C99 Miscellaneous

• PM: equilibrium point, id=3815 -- WP guess: equilibrium point -- Status:

• PM: Hartman-Grobman theorem, id=3816 -- WP guess: Hartman-Grobman theorem -- Status:

• PM: nullcline, id=5972 -- WP guess: nullcline -- Status:

• PM: stable manifold theorem, id=3315 -- WP: stable manifold theorem -- Status: NM

linas 17:27, 9 June 2006 (UTC)

• PM: attractor, id=7089 -- WP guess: attractor -- Status:

34D20 Lyapunov stability

• PM: Lyapunov stable, id=3535 -- WP: Lyapunov stable -- Status: A

linas 15:55, 9 June 2006 (UTC)

• PM: neutrally stable fixed point, id=3537 -- WP: neutrally stable fixed point -- Status: A

linas 16:34, 9 June 2006 (UTC)

• PM: stable fixed point, id=3536 -- WP: stable fixed point -- Status: A

linas 16:24, 9 June 2006 (UTC)

34D30 Structural stability and analogous concepts

• PM: structural stability, id=4535 -- WP: structural stability -- Status: C

The whole thing has been copied by someone else (User:Rich Farmbrough), so I suppose this tag is appropriate. Jeekc 10:50, 15 December 2005 (UTC)

34L05 General spectral theory

• PM: Gelfand spectral radius theorem, id=4309 -- WP guess: Gelfand spectral radius theorem -- Status:

• PM: proof of Gelfand spectral radius theorem, id=7469 -- WP: Gelfand spectral radius theorem -- Status: N

Its a proof, current policy has it that we don't do proofs. linas 17:10, 9 June 2006 (UTC)

34L15 Estimation of eigenvalues, upper and lower bounds

• PM: Rayleigh quotient, id=4308 -- WP guess: Rayleigh quotient -- Status:

34L40 Particular operators (Dirac, one-dimensional Schrödinger, etc.)

• PM: Dirac delta function, id=1491 -- WP: Dirac delta function -- Status: A

linas 00:13, 8 June 2006 (UTC)

34M05 Entire and meromorphic solutions

• PM: Hermite equation, id=7058 -- WP guess: Hermite equation -- Status: