EQUIVALENCE AND NORMAL FORMS OF GERMS OF SMOOTH MAPPINGS

ContentsIntroductionChapter I §1. Normal forms of formal series §2. Normal forms of germs of smooth mappingsChapter II §1. One-sided equivalence §2. Two-sided equivalence §3. Conjugacy of germs of smooth mappings §4. Linearization §5. Families and versalityChapter III §1. Small operators §2. Bounded operators and small operators in the space of germs of smooth mappings §3. Proofs of the theorems on right and two-sided equivalence §4. Proofs of the theorems on conjugacyReferences

[1]  A. N. Varčenko LOCAL TOPOLOGICAL PROPERTIES OF DIFFERENTIABLE MAPPINGS , 1974 .

[2]  P. Hartman Ordinary Differential Equations , 1965 .

[3]  Shlomo Sternberg,et al.  Local Contractions and a Theorem of Poincare , 1957 .

[4]  Shlomo Sternberg,et al.  On the Structure of Local Homeomorphisms of Euclidean n-Space, II , 1958 .

[5]  M. Gromov STABLE MAPPINGS OF FOLIATIONS INTO MANIFOLDS , 1969 .

[6]  P. Hartman A lemma in the theory of structural stability of differential equations , 1960 .

[7]  A N Varčenko,et al.  THEOREMS ON THE TOPOLOGICAL EQUISINGULARITY OF FAMILIES OF ALGEBRAIC VARIETIES AND FAMILIES OF POLYNOMIAL MAPPINGS , 1972 .

[8]  Vladimir I. Arnold,et al.  CRITICAL POINTS OF SMOOTH FUNCTIONS AND THEIR NORMAL FORMS , 1975 .

[9]  Shlomo Sternberg,et al.  THE STRUCTURE OF LOCAL HOMEOMORPHISMS, III*1 , 1959 .

[10]  Ja M Èliašberg,et al.  ON SINGULARITIES OF FOLDING TYPE , 1970 .

[11]  V. Poénaru On Regular Homotopy in Codimension 1 , 1966 .

[12]  Anthony Phillips Submersions of open manifolds , 1967 .

[13]  M. Gromov,et al.  Embeddings and immersions in Riemannian geometry , 1970 .

[14]  R. I. Bogdanov Versal deformations of a singular point of a vector field on the plane in the case of zero eigenvalues , 1975 .

[15]  Harold Levine,et al.  Singularities of differentiable mappings , 1971 .

[16]  F. Takens Partially hyperbolic fixed points , 1971 .

[17]  Richard J Venti Linear normal forms of differential equations , 1966 .

[18]  P. Hartman On the local linearization of differential equations , 1963 .

[19]  Floris Takens,et al.  Normal forms for certain singularities of vectorfields , 1973 .

[20]  M. Hirsch Immersions of manifolds , 1959 .

[21]  R. I. Bogdanov Reduction to orbital normal form of a vector field on the plane , 1976 .

[22]  G. Belitskii Functional equations and conjugacy of local diffeomorphisms of a finite smoothness class , 1973 .

[23]  S. Smale The Classification of Immersions of Spheres in Euclidean Spaces , 1959 .

[24]  Kuo-Tsai Chen,et al.  EQUIVALENCE AND DECOMPOSITION OF VECTOR FIELDS ABOUT AN ELEMENTARY CRITICAL POINT. , 1963 .

[25]  G. R. Belickiĭ FUNCTIONAL EQUATIONS AND LOCAL CONJUGACY OF MAPPINGS OF CLASS $C^{\infty}$ , 1973 .

[26]  V. Arnold SINGULARITIES OF SMOOTH MAPPINGS , 1968 .

[27]  V. Arnold LECTURES ON BIFURCATIONS IN VERSAL FAMILIES , 1972 .

[28]  H. Dulac Solutions d'un système d'équations différentielles dans le voisinage de valeurs singulières , 1912 .