Analytic Invariant Curves Research Articles

Analytic classification of germs of parabolic antiholomorphic diffeomorphisms of codimension k

AbstractWe investigate the local dynamics of antiholomorphic diffeomorphisms around a parabolic fixed point. We first give a normal form. Then we give a complete classification including a modulus space for antiholomorphic germs with a parabolic fixed point under analytic conjugacy. We then study some geometric applications: existence of real analytic invariant curves, existence of holomorphic and antiholomorphic roots of holomorphic and antiholomorphic parabolic germs, and commuting holomorphic and antiholomorphic parabolic germs.

Analytic Invariant Curves for an Iterative Equation Related to Ricker-type Second-order Equation

Analytic Invariant Curves for an Iterative Equation Related to Ricker-type Second-order Equation

Analytic invariant curves for a second order difference equation modelled from macroeconomics under the Brjuno condition

In this paper, we investigate analytic invariant curves of a planar mapping which derives a second order difference equation modelled from macroeconomics under the Brjuno condition that is weaker than the Diophantine condition, and present analytic invariant curves by constructing uniformly convergent power series.

Analytic invariant curves for an iterative equation related to dissipative standard map

In this paper, we study existence of invariant curves of an iterative equation urn:x-wiley:mma:media:mma4260:mma4260-math-0001 which is from dissipative standard map. By constructing an invertible analytic solution g(x) of an auxiliary equation of the form urn:x-wiley:mma:media:mma4260:mma4260-math-0002 invertible analytic solutions of the form g(λg − 1(x)) for the original iterative functional equation are obtained. Besides the hyperbolic case 0 < |λ| < 1, we focus on those λ on the unit circle S1, that is, |λ| = 1. We discuss not only those λ at resonance, that is, at a root of the unity, but also those λ near resonance under the Brjuno condition. Copyright © 2016 John Wiley & Sons, Ltd.

Small divisors problem in dynamical systems and analytic invariant curves for an iterative equation related to a rational difference equation

We study the existence of analytic invariant curves of the iterative equation f(f(x)) = ax/(f(x)x + b), which arises from second-order rational difference equations. By reducing the equation with the Schroder transformation to an auxiliary equation we discuss not only the constant α at resonance, that is, at a root of the unity, but also those α near resonance under the Bryuno condition.

Existence of analytic invariant curves for a complex planar mapping near resonance

In this paper a 2-dimensional mapping is investigated in the complex field ℂ for the existence of analytic invariant curves. Employing the method of majorant series, we need to discuss the eigenvalue α of the mapping at a fixed point. Besides the hyperbolic case , we focus on those α on the unit circle , i.e., . We discuss not only those α at resonance, i.e., at a root of the unity, but also those α near resonance under the Brjuno condition.

Analytic invariant curves for an iterative equation related to mosquito model

In this paper, we study the existence of analytic invariant curves of a iterative equation urn:x-wiley:1704214:media:mma3009:mma3009-math-0001 which from mosquito model. By constructing an invertible analytic solution g(x) of an auxiliary equation of the form urn:x-wiley:1704214:media:mma3009:mma3009-math-0002 invertible analytic solutions of the form g(αg − 1(x)) for the original iterative functional equation are obtained. Besides the hyperbolic case 0 < | α | < 1, we focus on those α on the unit circle S1, that is, | α | = 1. We discuss not only those α at resonance, that is at a root of the unity, but also those α near resonance under the Brjuno condition. Copyright © 2013 John Wiley & Sons, Ltd.

Analytic invariant curves for an iterative equation related to Pielou's equation

In this paper, we study the existence of analytic invariant curves of an iterative equation which is from Pielou's equation. By reducing the equation with the Schröder transformation to an auxiliary equation, the author discusses not only that the constant at resonance, i.e. at a root of the unity, but also those near resonance under the Brjuno condition.

The Existence of Analytic Invariant Curves for a Planar Map

In this paper, we study the existence of analytic invariant curves for two-dimensional maps in the complex field C. Employing the method of majorant series, we discuss the eigenvalueof the mapping at a fixed point. We discuss not only thoseat resonance, i.e., at a root of the unity but also thosenear resonance under Brjuno condition.

Normal Forms of Foliations and Curves Defined by a Function with a Generic Tangent Cone

We first describe the local and global moduli spaces of germs of foliations defined by analytic functions in two variables with p transverse smooth branches, and with integral multiplicities (in the univalued holomorphic case) or complex multiplicities (in the multivalued “Darboux” case). We specify normal forms in each class. Then we study on these moduli space the distribution C induced by the following equivalence relation: two points are equivalent if and only if the corresponding foliations have the same analytic invariant curves up to analytical conjugacy. Therefore, the space of leaves of C is the moduli space of curves. We prove that C is rationally integrable. These rational integrals give a complete system of invariants for these generic plane curves, which extend the well-known cross-ratios between branches. 2000 Math. Subj. Class. 34M35, 32S65, 32G13.

Analytic invariant curves of a nonlinear second order difference equation

This article studies the existence of analytic invariant curves for a nonlinear second order difference equation which was modeled from macroeconomics of the business cycle. The author not only discusses the case of the eigenvalue off the unit circle S 1 and the case on S 1 with the Diophantine condition but also considers the case of the eigenvalue at a root of the unity, which obviously violates the Diophantine condition.

Analytic invariant curves for a planar mapping

This paper is concerned with the existence of analytic invariant curves for a planar mapping. By constructing a convergent power series solution of an auxiliary equation, analytic solutions of the original equation are obtained. In this paper, we discuss not only the general case, but also the critical cases as well, in particular, the case where β is a unit root is discussed.

Analytic invariant curves for a planar map

In this paper, we study the existence of analytic invariant curves for two-dimensional maps of the form F( x, y) = ( x + y, y + G( x) + H( x + y)).