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Pitchfork bifurcationBifurcation theoryCatastrophe theoryHopf bifurcationBifurcation diagramSaddle-node bifurcationSymmetry breakingFeigenbaum constantsRegular singular pointEigenvalue perturbationTranscendental number theoryClass field theoryBoundary value problemElliptic boundary value problemTranscendental equationStationary pointDendriteSingularitySystem of bilinear equationsStefan problemRemovable singularityDirac delta functionSecond partial derivative testOptical vortexLimit cycleQuantum critical pointAlternating multilinear mapBiharmonic equationGeometric flowRicci flowIndicator functionNoncommutative geometryLiouville field theoryEquilibrium pointAlgebraic analysisAsymptoteQuantum phase transitionIntegral curveDivision algebraPeriod-doubling bifurcationMultifractal systemSingular solutionCritical dimensionInflection pointRiemann hypothesisImproper integralSpectral graph theoryDynamical systems theoryBkl singularityPhase spaceHyperbolaComplete bipartite graphFixed-point theoremsHilbert's nullstellensatzRiemannian geometrySpectrumIntersection theoryMatrix differential equationDirichlet problemHarmonic polynomialMonotone convergence theoremPseudo-euclidean spaceFredholm integral equationNewton fractalEigenfunctionHolomorphic functionConfluent hypergeometric functionLinear stabilityCauchy horizonAlgebraic number fieldLinear independenceClassical field theoryDerivative testStability theoryOscillationResultantBirational geometryNullclineFractal derivativeSymplectic geometryHomeomorphismLower limit topologyBregman divergenceFractalFrobenius algebraInitial value theoremEuclidean domainOrdinary differential equationStein manifoldExact differential equationTopological quantum field theoryResolvent formalismPerfectoid spaceInvariant manifoldLinear functionResidueReal analysisPrimitive element theoremAlternating series testField norm