Overstability and resonance

Augustin Fruchard; Reinhard Schäfke

Displaying similar documents to “Overstability and resonance”

The analytic $α$ -capacity and the Cauchy integral

K. Adžievski (1986)

Matematički Vesnik

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Solutions of non-homogeneous linear differential equations in the unit disc

Ting-Bin Cao, Zhong-Shu Deng (2010)

Annales Polonici Mathematici

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The main purpose of this paper is to consider the analytic solutions of the non-homogeneous linear differential equation $f^{(k)} + a_{k - 1} (z) f^{(k - 1)} + \dots + a ₁ (z) f^{'} + a ₀ (z) f = F (z)$ , where all coefficients $a ₀, a ₁, . . ., a_{k - 1}$ , F ≢ 0 are analytic functions in the unit disc = z∈ℂ: |z|<1. We obtain some results classifying the growth of finite iterated order solutions in terms of the coefficients with finite iterated type. The convergence exponents of zeros and fixed points of solutions are also investigated.

Radii of p-valence of certain analytic functions of order $α$ with negative coefficients

M. K. Aouf (1989)

Matematički Vesnik

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Algebraic and analytic properties of solutions of abstract differential equations

R. Bittner

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CONTENTSINTRODUCTION............................................................................................................................... 3Chapter I. ALGEBRAIC PROPERTIES OF SOLUTIONS OF ABSTRACT DIFFERENTIALEQUATIONS§ 1. Ordinary abstract differential equations1. Taylor’s formula for an abstract derivative.......................................................................... 42 π-solutions....................................................................................................................................

Persistence of fixed points under rigid perturbations of maps

Salvador Addas-Zanata, Pedro A. S. Salomão (2014)

Fundamenta Mathematicae

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Let f: S¹ × [0,1] → S¹ × [0,1] be a real-analytic diffeomorphism which is homotopic to the identity map and preserves an area form. Assume that for some lift f̃: ℝ × [0,1] → ℝ × [0,1] we have Fix(f̃) = ℝ × 0 and that f̃ positively translates points in ℝ × 1. Let $f ̃_{ϵ}$ be the perturbation of f̃ by the rigid horizontal translation (x,y) ↦ (x+ϵ,y). We show that $F i x (f ̃_{ϵ}) = \emptyset$ for all ϵ > 0 sufficiently small. The proof follows from Kerékjártó’s construction of Brouwer lines for orientation preserving...

Separately analytic functions and envelopes of holomorphy of some lower dimensional subsets of $C^{n}$

J. Siciak (1969)

Annales Polonici Mathematici

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Inclusion and neighborhood properties of certain subclasses of p-valent functions of complex order defined by convolution

R. M. El-Ashwah, M. K. Aouf, S. M. El-Deeb (2011)

Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica

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In this paper we introduce and investigate three new subclasses of $p$ -valent analytic functions by using the linear operator $D_{λ, p}^{m} (f * g) (z)$ . The various results obtained here for each of these function classes include coefficient bounds, distortion inequalities and associated inclusion relations for $(n, θ)$ -neighborhoods of subclasses of analytic and multivalent functions with negative coefficients, which are defined by means of a non-homogenous differential equation.

Local analytic solutions of the functional equation $Φ (z) = H (z; Φ [f_{1} (z)], . . ., Φ [f_{m} (z)])$

Wilhelmina Smajdor (1970)

Annales Polonici Mathematici

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The Lindelöf property and σ-fragmentability

B. Cascales, I. Namioka (2003)

Fundamenta Mathematicae

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In the previous paper, we, together with J. Orihuela, showed that a compact subset X of the product space ${[- 1, 1]}^{D}$ is fragmented by the uniform metric if and only if X is Lindelöf with respect to the topology γ(D) of uniform convergence on countable subsets of D. In the present paper we generalize the previous result to the case where X is K-analytic. Stated more precisely, a K-analytic subspace X of ${[- 1, 1]}^{D}$ is σ-fragmented by the uniform metric if and only if (X,γ(D)) is Lindelöf, and if this is...

Relations between the boundary values and periods for generalized analytic functions in $R^{n}$

Wolfgang Tutschke (1983)

Banach Center Publications

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A new necessary condition for analytic varieties satisfying the local Phragmén-Lindelöf condition

Tobias Heinrich (2005)

Annales Polonici Mathematici

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For an analytic variety V in ℂⁿ containing the origin which satisfies the local Phragmén-Lindelöf condition $P L_{l o c} (0)$ it is shown that for each real simple curve γ and each d ≥ 1 the limit variety $T_{γ, d} V$ satisfies the strong Phragmén-Lindelöf condition (SPL).

On the group of real analytic diffeomorphisms

Takashi Tsuboi (2009)

Annales scientifiques de l'École Normale Supérieure

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The group of real analytic diffeomorphisms of a real analytic manifold is a rich group. It is dense in the group of smooth diffeomorphisms. Herman showed that for the $n$ -dimensional torus, its identity component is a simple group. For $U (1)$ fibered manifolds, for manifolds admitting special semi-free $U (1)$ actions and for 2- or 3-dimensional manifolds with nontrivial $U (1)$ actions, we show that the identity component of the group of real analytic diffeomorphisms is a perfect group.

Real and complex analytic sets. The relevance of Segre varieties

Klas Diederich, Emmanuel Mazzilli (2008)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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Let $X \subset {ℂ^{n}}^{n}$ be a closed real-analytic subset and put $𝒜 : = {z \in X ∣ \exists A \subset X, germ of a complex-analytic set, z \in A, {dim}_{z} A > 0}$ This article deals with the question of the structure of $𝒜$ . In the main result a natural proof is given for the fact, that $𝒜$ always is closed. As a main tool an interesting relation between complex analytic subsets of $X$ of positive dimension and the Segre varieties of $X$ is proved and exploited.

On certain subclasses of analytic functions associated with the Carlson–Shaffer operator

Jagannath Patel, Ashok Kumar Sahoo (2014)

Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica

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The object of the present paper is to solve Fekete-Szego problem and determine the sharp upper bound to the second Hankel determinant for a certain class $R^{λ} (a, c, A, B)$ of analytic functions in the unit disk. We also investigate several majorization properties for functions belonging to a subclass ${\tilde{R}}^{λ} (a, c, A, B)$ of $R^{λ} (a, c, A, B)$ and related function classes. Relevant connections of the main results obtained here with those given by earlier workers on the subject are pointed out.

Perturbation of analytic operators and temporal regularity of discrete heat kernels

Sönke Blunck (2000)

Colloquium Mathematicae

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In analogy to the analyticity condition $∥ A e^{t A} ∥ \leq C t^{- 1}$ , t > 0, for a continuous time semigroup ${(e^{t A})}_{t \geq 0}$ , a bounded operator T is called analytic if the discrete time semigroup ${(T^{n})}_{n \in ℕ}$ satisfies $∥ (T - I) T^{n} ∥ \leq C n^{- 1}$ , n ∈ ℕ. We generalize O. Nevanlinna’s characterization of powerbounded and analytic operators T to the following perturbation result: if S is a perturbation of T such that $∥ R (λ_{0}, T) - R (λ_{0}, S) ∥$ is small enough for some $λ_{0} \in ϱ (T) \cap ϱ (S)$ , then the type $ω$ of the semigroup $(e^{t (S - I)})$ also controls the analyticity of S in the sense that $∥ (S - I) S^{n} ∥ \leq C (ω + n^{- 1}) e^{ω n}$ , n ∈ ℕ. As an application...

The Behavior of Rigid Analytic Functions Around Orbits of Elements of < $> ℂ_{p} <$ >

S. Achimescu, V. Alexandru, N. Popescu, M. Vâjâitu, A. Zaharescu (2012)

Rendiconti del Seminario Matematico della Università di Padova

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Analytic solutions of a nonlinear two variables difference system whose eigenvalues are both 1

Mami Suzuki (2011)

Annales Polonici Mathematici

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For nonlinear difference equations, it is difficult to obtain analytic solutions, especially when all the eigenvalues of the equation are of absolute value 1. We consider a second order nonlinear difference equation which can be transformed into the following simultaneous system of nonlinear difference equations: ⎧ x(t+1) = X(x(t),y(t)) ⎨ ⎩ y(t+1) = Y(x(t), y(t)) where $X (x, y) = λ ₁ x + μ y + \sum_{i + j \geq 2} c_{i j} x^{i} y^{j}$ , $Y (x, y) = λ ₂ y + \sum_{i + j \geq 2} d_{i j} x^{i} y^{j}$ satisfy some conditions. For these equations, we have obtained analytic solutions in the cases "|λ₁| ≠ 1 or |λ₂|...