Displaying similar documents to “Analytic cell decomposition and analytic motivic integration”

Extending Tamm's theorem

Lou van den Dries, Chris Miller (1994)

Annales de l'institut Fourier

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We extend a result of M. Tamm as follows: Let f : A → ℝ , A ⊆ ℝ m + n , be definable in the ordered field of real numbers augmented by all real analytic functions on compact boxes and all power functions x ↦ x r : ( 0 , ∞ ) → ℝ , r ∈ ℝ . Then there exists N ∈ ℕ such that for all ( a , b ) ∈ A , if y ↦ f ( a , y ) is C N in a neighborhood of b , then y ↦ f ( a , y ) is real analytic in a neighborhood of b .

A p -adic approach to local analytic dynamics: analytic conjugacy of analytic maps tangent to the identity

Adrian Jenkins, Steven Spallone (2009)

Annales de la faculté des sciences de Toulouse Mathématiques

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In this note, we consider the question of local analytic equivalence of analytic functions which fix the origin and are tangent to the identity. All mappings and equivalences are considered in the non-archimedean context e.g. all norms can be considered p -adic norms. We show that any two mappings f and g which are formally equivalent are also analytically equivalent. We consider the related questions of roots and centralizers for analytic mappings. In this setting, anything which can...

On global Nash functions

Jesús M. Ruiz, Masahiro Shiota (1994)

Annales scientifiques de l'École Normale Supérieure

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Relations among analytic functions. I

Edward Bierstone, P. D. Milman (1987)

Annales de l'institut Fourier

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Neither real analytic sets nor the images of real or complex analytic mappings are, in general, coherent. Let Φ : X → Y be a morphism of real analytic spaces, and let Ψ : 𝒢 → ℱ be a homomorphism of coherent modules over the induced ring homomorphism Φ * : 𝒪 Y → 𝒪 X . We conjecture that, despite the failure of coherence, certain natural discrete invariants of the modules of formal relations ℛ a = Ker Ψ ^ a , a ∈ X , are upper semi-continuous in the analytic Zariski topology of X . We prove semicontinuity in many cases (e.g. in the algebraic...