{"name": "积分方程", "children": [{"name": "偏微分方程", "children": [{"name": "δ-诺伊曼问题", "en": "δ-Neumann problem", "superfield": "数学"}, {"name": "一致双曲性", "en": "uniform hyperbolicity", "superfield": "数学"}, {"name": "一致抛物性", "en": "uniform parabolicity", "superfield": "数学"}, {"name": "一致椭圆性", "en": "uniform ellipticity", "superfield": "数学"}, {"name": "一阶偏微分方程", "en": "partial differential equation of first order", "superfield": "数学"}, {"name": "不适定问题", "en": "ill-posed problem", "superfield": "数学"}, {"name": "严格亚椭圆", "en": "strictly hypoelliptic", "superfield": "数学"}, {"name": "严格双曲性", "en": "strict hyperbolicity", "superfield": "数学"}, {"name": "主型算子", "en": "operator of principal type", "superfield": "数学"}, {"name": "二阶偏微分方程", "en": "partial differential equation of second order", "superfield": "数学"}, {"name": "亚椭圆算子", "en": "hypoelliptic operator", "superfield": "数学"}, {"name": "仿微分算子", "en": "paradifferential operator", "superfield": "数学"}, {"name": "伪微分方程", "en": "pseudo-differential equation", "superfield": "数学"}, {"name": "伪微分算子", "en": "pseudo-differential operator", "superfield": "数学"}, {"name": "伯格方程", "en": "Burger equation", "superfield": "数学"}, {"name": "伯格曼算子", "en": "Bergman operator", "superfield": "数学"}, {"name": "伴随微分方程", "en": "adjoint differential equation", "superfield": "数学"}, {"name": "伴随微分算子", "en": "adjoint differential operator", "superfield": "数学"}, {"name": "余法向导数", "en": "conormal derivative", "superfield": "数学"}, {"name": "依赖[区]域", "en": "domain of dependence", "superfield": "数学"}]}, {"name": "动力系统（数学）", "children": [{"name": "Ω稳定性", "en": "Ω-stability", "superfield": "数学"}, {"name": "α极限集合", "en": "α-limit set", "superfield": "数学"}, {"name": "λ引理", "en": "λ-lemma", "superfield": "数学"}, {"name": "ω极限集合", "en": "ω-limit set", "superfield": "数学"}, {"name": "位移自同构", "en": "shift automorphism", "superfield": "数学"}, {"name": "公理A", "en": "axiom A", "superfield": "数学"}, {"name": "冲击函数", "en": "bump function", "superfield": "数学"}, {"name": "动力[学]方程", "en": "equation of dynamics", "superfield": "数学"}, {"name": "动力系统", "en": "dynamical system", "superfield": "数学"}, {"name": "半流", "en": "semi-flow", "superfield": "数学"}, {"name": "双曲不动点", "en": "hyperbolic fixed point", "superfield": "数学"}, {"name": "双曲不变集", "en": "hyperbolic invariant set", "superfield": "数学"}, {"name": "双曲周期点", "en": "hyperbolic periodic point", "superfield": "数学"}, {"name": "双曲奇点", "en": "hyperbolic singularity", "superfield": "数学"}, {"name": "双曲环体自同构", "en": "hyperbolic toral automorphism", "superfield": "数学"}, {"name": "双曲线性映射", "en": "hyperbolic linear map", "superfield": "数学"}, {"name": "双曲结构", "en": "hyperbolic structure", "superfield": "数学"}, {"name": "双曲闭轨", "en": "hyperbolic closed orbit", "superfield": "数学"}, {"name": "可扩映射", "en": "expansive map", "superfield": "数学"}, {"name": "同宿点", "en": "homoclinic point", "superfield": "数学"}]}, {"name": "常微分方程", "children": [{"name": "KAM理论", "en": "Kolmogorov-Arnold-Moser theory", "superfield": "数学"}, {"name": "SL问题", "en": "Sturm-Liouville boundary problem", "superfield": "数学"}, {"name": "α极限点", "en": "α-limit point", "superfield": "数学"}, {"name": "ω极限点", "en": "ω-limit point", "superfield": "数学"}, {"name": "一致稳定性", "en": "uniform stability", "superfield": "数学"}, {"name": "一阶线性微分方程", "en": "linear differential equation of first order", "superfield": "数学"}, {"name": "上调和解", "en": "superharmonic solution", "superfield": "数学"}, {"name": "下调和解", "en": "subharmonic solution", "superfield": "数学"}, {"name": "不变中心流形", "en": "invariant central manifold", "superfield": "数学"}, {"name": "不变流形", "en": "invariant manifold", "superfield": "数学"}, {"name": "不变环面", "en": "invariant torus", "superfield": "数学"}, {"name": "久期项", "en": "secular term", "superfield": "数学"}, {"name": "代数微分方程", "en": "algebraic differential equation", "superfield": "数学"}, {"name": "伯努利微分方程", "en": "Bernoulli differential equation", "superfield": "数学"}, {"name": "佩亚诺存在定理", "en": "Peano existence theorem", "superfield": "数学"}, {"name": "保守微分方程", "en": "conservative differential equation", "superfield": "数学"}, {"name": "保面积映射", "en": "area-preserving mapping", "superfield": "数学"}, {"name": "克莱罗微分方程", "en": "Clairaut differential equation", "superfield": "数学"}, {"name": "全局稳定性", "en": "global stability", "superfield": "数学"}, {"name": "共振现象", "en": "resonance phenomenon", "superfield": "数学"}]}, {"name": "特殊函数", "children": [{"name": "P函数", "en": "P-function", "superfield": "数学"}, {"name": "q展开式", "en": "q-expansion formula", "superfield": "数学"}, {"name": "Γ函数", "en": "gamma-function", "superfield": "数学"}, {"name": "β函数", "en": "β-function", "superfield": "数学"}, {"name": "σ函数", "en": "σ-function", "superfield": "数学"}, {"name": "三Γ函数", "en": "trigamma-function", "superfield": "数学"}, {"name": "上升算子", "en": "slip up operator", "superfield": "数学"}, {"name": "下降算子", "en": "slip down operator", "superfield": "数学"}, {"name": "不完全Γ函数", "en": "incomplete Γ-function", "superfield": "数学"}, {"name": "不完全β函数", "en": "incomplete β-function", "superfield": "数学"}, {"name": "伯努利多项式", "en": "Bernoulli polynomial", "superfield": "数学"}, {"name": "伯努利数", "en": "Bernoulli number", "superfield": "数学"}, {"name": "余σ函数", "en": "co-sigma-function", "superfield": "数学"}, {"name": "余弦积分", "en": "cosine integral", "superfield": "数学"}, {"name": "傅里叶-贝塞尔级数", "en": "Fourier-Bessel series", "superfield": "数学"}, {"name": "兰登变换", "en": "Landen transformation", "superfield": "数学"}, {"name": "切比雪夫微分方程", "en": "Chebyshev differential equation", "superfield": "数学"}, {"name": "勒让德-雅可比标准型", "en": "Legendre-Jacobi standard form", "superfield": "数学"}, {"name": "勒让德关系", "en": "Legendre relation", "superfield": "数学"}, {"name": "勒让德多项式", "en": "Legendre polynomial", "superfield": "数学"}]}, {"name": "积分方程", "children": []}, {"name": "函数方程", "en": "functional equation", "superfield": "数学"}, {"name": "卡莱曼型核", "en": "kernel of Carleman type", "superfield": "数学"}, {"name": "叠核", "en": "iterated kernel", "superfield": "数学"}, {"name": "可分核", "en": "separated kernel", "superfield": "数学"}, {"name": "哈默斯坦积分方程", "en": "Hammerstein integral equation", "superfield": "数学"}, {"name": "埃尔米特型核", "en": "Hermitian kernel", "superfield": "数学"}, {"name": "奇[异]核", "en": "singular kernel", "superfield": "数学"}, {"name": "奇异积分方程", "en": "singular integral equation", "superfield": "数学"}, {"name": "对称核", "en": "symmetric kernel", "superfield": "数学"}, {"name": "希尔伯特-施密特型核", "en": "kernel of Hilbert-Schmidt type", "superfield": "数学"}, {"name": "希尔伯特-施密特展开定理", "en": "Hilbert-Schmidt expansion theorem", "superfield": "数学"}, {"name": "弗雷德霍姆r次余子式", "en": "Fredholm r-th minor", "superfield": "数学"}, {"name": "弗雷德霍姆初余子式", "en": "Fredholm first minor", "superfield": "数学"}, {"name": "弗雷德霍姆型积分微分方程", "en": "integro-differential equation of Fredholm type", "superfield": "数学"}, {"name": "弗雷德霍姆择一定理", "en": "Fredholm alternative theorem", "superfield": "数学"}, {"name": "弗雷德霍姆积分方程", "en": "Fredholm integral equation", "superfield": "数学"}, {"name": "弗雷德霍姆行列式", "en": "Fredholm determinant", "superfield": "数学"}, {"name": "恩斯库格法", "en": "Enskog method", "superfield": "数学"}, {"name": "普朗特积分微分方程", "en": "Prandtl integro-differential equation", "superfield": "数学"}, {"name": "本征值的指标", "en": "index of eigenvalues", "superfield": "数学"}]}