Tame semiflows for piecewise linear vector fields

Daniel Panazzolo

Displaying similar documents to “Tame semiflows for piecewise linear vector fields”

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 $f : A \to ℝ, A \subseteq ℝ^{m + n}$ , be definable in the ordered field of real numbers augmented by all real analytic functions on compact boxes and all power functions $x \mapsto x^{r} : (0, \infty) \to ℝ, r \in ℝ$ . Then there exists $N \in ℕ$ such that for all $(a, b) \in A$ , if $y \mapsto f (a, y)$ is $C^{N}$ in a neighborhood of $b$ , then $y \mapsto f (a, y)$ is real analytic in a neighborhood of $b$ .

Decompositions of $E^{3}$ which satisfy a uniform Lipschitz condition are factors of $E^{4}$

Ralph Bean (1971)

Fundamenta Mathematicae

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Pieri-type intersection formulas and primary obstructions for decomposing 2-forms

Sinan Sertöz (2001)

Colloquium Mathematicae

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We study the homological intersection behaviour for the Chern cells of the universal bundle of G(d,Qₙ), the space of [d]-planes in the smooth quadric Qₙ in $ℙ^{n + 1}$ over the field of complex numbers. For this purpose we define some auxiliary cells in terms of which the intersection properties of the Chern cells can be described. This is then applied to obtain some new necessary conditions for the global decomposability of a 2-form of constant rank.

Semi-monotone sets

Saugata Basu, Andrei Gabrielov, Nicolai Vorobjov (2013)

Journal of the European Mathematical Society

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A coordinate cone in $ℝ^{n}$ is an intersection of some coordinate hyperplanes and open coordinate half-spaces. A semi-monotone set is an open bounded subset of $ℝ^{n}$ , definable in an o-minimal structure over the reals, such that its intersection with any translation of any coordinate cone is connected. This notion can be viewed as a generalization of convexity. Semi-monotone sets have a number of interesting geometric and combinatorial properties. The main result of the paper is that every semi-monotone...

$L^{p} - L^{q}$ estimates for functions of the Laplace-Beltrami operator on noncompact symmetric spaces. III

Michael Cowling, Saverio Giulini, Stefano Meda (2001)

Annales de l’institut Fourier

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Let $X$ be a symmetric space of the noncompact type, with Laplace–Beltrami operator $- ℒ$ , and let $[b, \infty)$ be the $L^{2} (X)$ -spectrum of $ℒ$ . For $τ$ in $ℂ$ such that $Re τ \geq 0$ , let $𝒫_{τ}$ be the operator on $L^{2} (X)$ defined formally as $\exp (- τ {(ℒ - b)}^{1 / 2})$ . In this paper, we obtain $L^{p} - L^{q}$ operator norm estimates for $𝒫_{τ}$ for all $τ$ , and show that these are optimal when $τ$ is small and when $| \arg τ |$ is bounded below $π / 2$ .

Cell decomposition for two dimensional local fields

Ali Bleybel (2007)

Rendiconti del Seminario Matematico della Università di Padova

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Solvability near the characteristic set for a class of planar vector fields of infinite type

Alberto P. Bergamasco, Abdelhamid Meziani (2005)

Annales de l’institut Fourier

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We study the solvability of equations associated with a complex vector field $L$ in $ℝ^{2}$ with $C^{\infty}$ or $C^{ω}$ coefficients. We assume that $L$ is elliptic everywhere except on a simple and closed curve $Σ$ . We assume that, on $Σ$ , $L$ is of infinite type and that $L \land \bar{L}$ vanishes to a constant order. The equations considered are of the form $L u = p u + f$ , with $f$ satisfying compatibility conditions. We prove, in particular, that when the order of vanishing of $L \land \bar{L}$ is $> 1$ , the equation $L u = f$ is solvable in the $C^{\infty}$ category but not in the...

Expansions of o-minimal structures by sparse sets

Harvey Friedman, Chris Miller (2001)

Fundamenta Mathematicae

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Given an o-minimal expansion ℜ of the ordered additive group of real numbers and E ⊆ ℝ, we consider the extent to which basic metric and topological properties of subsets of ℝ definable in the expansion (ℜ,E) are inherited by the subsets of ℝ definable in certain expansions of (ℜ,E). In particular, suppose that $f (E^{m})$ has no interior for each m ∈ ℕ and $f : ℝ^{m} \to ℝ$ definable in ℜ, and that every subset of ℝ definable in (ℜ,E) has interior or is nowhere dense. Then every subset of ℝ definable in (ℜ,(S))...