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Stability theorySingular solutionEigenvalue perturbationSpectrumLinear differential equationLasalle's invariance principleStable manifoldEigenvalueMarginal stabilityEigenvalues and eigenvectorsEigenfunctionBiharmonic equationStochastic differential equationLinear time-invariant systemL-stabilityTranscritical bifurcationHarmonic mapLax pairElliptic boundary value problemStiff equationRegular singular pointSemi-implicit euler methodLyapunov functionOscillation theorySmall-gain theoremQuadratic functionDegenerate bilinear formCharacteristic polynomialSpectral theoremImplicit functionLinear mapBifurcation diagramContinuous linear operatorLinearityEssential spectrumLinear functionMatrix differential equationDirichlet energyErnst equationDiscrete spectrumOrdinary differential equationQuasiconvex functionSaddle-node bifurcationHopf bifurcationTranscendental equationEquilibrium pointAlgebraic riccati equationAiry equationPositive linear functionalStationary pointBessel functionLinear relationRiccati equationSpectral graph theoryLyapunov exponentStable distributionAbel's identityK-stabilityStructural stabilityElasticity of a functionExact differential equationProbability amplitudeStochastic matrixRunge's phenomenonRandom dynamical systemInvertible matrixLimit cycleNonlinear systemCharacteristic equationSine-gordon equationInvariant manifoldMagnus expansionSelf-adjoint operatorCrisisLangevin equationStefan problemOrbit-stabilizer theoremD'alembert's formulaExplicit symmetry breakingAlternating multilinear mapComplex numberOscillationRadial curveQuadratic growthQuadratic formMorse functionAttractorHilbert transformSingular valueAlgebraic functionNonlinear programmingRicci flowFredholm integral equationLocal linearization methodStationary processNonlinear regressionOseledets theoremDynamical systems theoryLinear systemCauchy-schwarz inequality