scholarly journals Invariant curves around a parabolic fixed point at infinity

1990 ◽  
Vol 10 (2) ◽  
pp. 209-229 ◽  
Author(s):  
Dov Aharonov ◽  
Uri Elias
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Invariant Curves ◽  
The Stability ◽  
Area Preserving ◽  
Parabolic Fixed Point

AbstractThe stability of a fixed point of an area-preserving transformation in the plane is characterized by the invariant curves which surround it. The existence of invariant curves had been extensively studied for elliptic fixed points. Here we study the similar problem for parabolic fixed points. In particular we are interested in the case where the fixed point is at infinity.

scholarly journals Parabolic fixed points, invariant curves and action-angle variables

1990 ◽  
Vol 10 (2) ◽  
pp. 231-245 ◽  
Author(s):  
Dov Aharonov ◽  
Uri Elias
Keyword(s):  
Fixed Point ◽  
Hamiltonian System ◽  
Fixed Points ◽  
Phase Flow ◽  
Invariant Curves ◽  
Elliptic Case ◽  
System A ◽  
Twist Mapping ◽  
Area Preserving ◽  
Parabolic Fixed Point

AbstractA fixed point of an area-preserving mapping of the plane is called elliptic if the eigenvalues of its linearization are of unit modulus but not ±1; it is parabolic if both eigenvalues are 1 or −1. The elliptic case is well understood by Moser's theory. Here we study when is a parabolic fixed point surrounded by closed invariant curves. We approximate our mapping T by the phase flow of an Hamiltonian system. A pair of variables, closely related to the action-angle variables, is used to reduce T into a twist mapping. The conditions for T to have closed invariant curves are stated in terms of the Hamiltonian.

New fixed point of on-orbit calibration scale based on the In-Bi eutectic alloy for application in novel high-stable space-borne standard sources

2021 ◽  
pp. 32-37
Author(s):  
Andrei A. Burdakin ◽  
Valerii R. Gavrilov ◽  
Ekaterina A. Us ◽  
Vitalii S. Bormashov
Keyword(s):  
Phase Transition ◽  
Fixed Point ◽  
Fixed Points ◽  
Eutectic Alloy ◽  
Earth Observation ◽  
Melt Temperature ◽  
Phase Transition Temperatures ◽  
Set Up ◽  
The Stability ◽  
Observation Space

The problem of ensuring stability of Earth observation space-borne instruments undertaking long-term temperature measurements within thermal IR spectral range is described. For in-flight reliable control of the space-borne IR instruments characteristics the stability of onboard reference sources should be improved. The function of these high-stable sources will be executed by novel onboard blackbodies, incorporating the melt↔freeze phase transition phenomenon, currently being developed. As a part of these works the task of realizing an on-orbit calibration scale within the dynamic temperature range of Earth observation systems 210−350 K based on fixed-point phase transition temperatures of a number of potentially suitable substances is advanced. The corresponding series of the onboard reference blackbodies will be set up on the basis of the on-orbit calibration scale fixed points. It is shown that the achievement of the target lies in carrying out a number of in-flight experiments with the selected fixed points and the prospective onboard fixed-point blackbodies prototypes. The new In-Bi eutectic alloy melt temperature fixed point (~345 K) is proposed as the significant fixed points of the future on-orbit calibration scale. The results of the new fixed point preliminary laboratory studies have been analyzed. The results allowed to start preparation of the in-flight experiments investigating the In-Bi alloy for the purpose of its application in the novel onboard reference sources.

Parabolic Fixed Points of Kleinian Groups and the Horospherical Foliation on Hyperbolic Manifolds

1997 ◽  
Vol 08 (02) ◽  
pp. 289-299 ◽  
Author(s):  
A. N. Starkov
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Limit Point ◽  
Elementary Proof ◽  
Hyperbolic Manifolds ◽  
Kleinian Groups ◽  
Complicated Structure ◽  
Constant Negative Curvature ◽  
Unit Tangent Bundle ◽  
Parabolic Fixed Point

We use dynamical approach to study parabolic fixed points of Kleinian groups Γ ⊂ Iso (ℍn). Let ℋ be the horospherical foliation on the unit tangent bundle SM of manifold M = Γ\ℍn with constant negative curvature. We construct examples Γ ⊂ Iso (ℍ4) which show that horosphere based at parabolic fixed point w ∈ ∂ℍ4 can project to leaf ℋx ⊂ SM of complicated structure: it can be locally closed and not closed; not locally closed and non-dense in the non-wandering set Ω+ ⊂ SM of ℋ; dense in Ω+ (this is equivalent to w being a horospherical limit point). Using the natural duality, one gets the corresponding examples of Γ-orbits on the light cone. We give an elementary proof of the fact that conical limit point w ∈ ∂ℍn cannot be a parabolic fixed point.

Linearization of holomorphic germs with quasi-parabolic fixed points

2008 ◽  
Vol 28 (3) ◽  
pp. 979-986 ◽  
Author(s):  
FENG RONG
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Fixed Points ◽  
Analytic Functions ◽  
Classical Result ◽  
Linear Part ◽  
Analytic Form ◽  
Moscow Math ◽  
Parabolic Fixed Point

AbstractLet f be a germ of a holomorphic diffeomorphism of $\mathbb {C}^n$ with the origin O being a quasi-parabolic fixed point, i.e. the spectrum of dfO consists of 1 and e2iπθj with $\theta _j\in \mathbb {R}\!\setminus \!\mathbb {Q}$. We show that f is locally holomorphically conjugated to its linear part, if f is of some particular form and its eigenvalues satisfy certain arithmetic conditions. When the spectrum of dfO does not consist of any 1’s, this is the classical result of Siegel [C. L. Siegel. Iteration of analytic functions. Ann. of Math.43 (1942), 607–612] and Brjuno [A. D. Brjuno. Analytic form of differential equations. Trans. Moscow Math. Soc.25 (1971), 131–288; 26 (1972), 199–239].

The even master system and generalized Kummer surfaces

1994 ◽  
Vol 116 (1) ◽  
pp. 131-142
Author(s):  
Jose Bertin ◽  
Pol Vanhaecke
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Algebraic Curves ◽  
Invariant Curves ◽  
Symmetric Form ◽  
Kummer Surface ◽  
Master System ◽  
Kummer Surfaces ◽  
Pass Through ◽  
Invariant Configuration

AbstractIn this paper we study a generalized Kummer surface associated to the Jacobian of those complex algebraic curves of genus two which admit an automorphism of order three. Such a curve can always be written as y2 = x6 + 2kx3 + 1 and k2 ╪ 1 is the modular parameter. The automorphism extends linearly to an automorphism of the Jacobian and we show that this extension has a 94 invariant configuration, i.e. it has 9 fixed points and 9 invariant theta curves, each of these curves contains 4 fixed points and 4 invariant curves pass through each fixed point. The quotient of the Jacobian by this automorphism has 9 singular points of type A2 and the 94 configuration descends to a 94 configuration of points and lines, reminiscent to the well-known 166 configuration on the Kummer surface. Our ‘generalized Kummer surface’ embeds in ℙ4 and is a complete intersection of a quadric and a cubic hypersurface. Equations for these hypersurfaces are computed and take a very symmetric form in well-chosen coordinates. This computation is done by using an integrable system, the ‘even master system’.

scholarly journals Fixed-Point Theorems for Multivalued Mappings in Modular Metric Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Parin Chaipunya ◽  
Chirasak Mongkolkeha ◽  
Wutiphol Sintunavarat ◽  
Poom Kumam
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Multivalued Mappings ◽  
Modular Metric Spaces ◽  
Contraction Type ◽  
The Stability

We give some initial properties of a subset of modular metric spaces and introduce some fixed-point theorems for multivalued mappings under the setting of contraction type. An appropriate example is as well provided. The stability of fixed points in our main theorems is also studied.

scholarly journals Recurrence and fixed points of surface homeomorphisms

1988 ◽  
Vol 8 (8) ◽  
pp. 99-107 ◽  
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Lebesgue Measure ◽  
Invariant Chain ◽  
Transitive Set ◽  
Surface Homeomorphisms ◽  
A Chain ◽  
Area Preserving ◽  
Twist Condition

AbstractWe prove that if f is a homeomorphism of the annulus which is homotopic to the identity and has a compact invariant chain transitive set L, then either f has a fixed point or every point of L moves uniformly in one direction: clockwise or counterclockwise. If f is area-preserving, then the annulus itself is a chain transitive set, so, in the presence of a boundary twist condition, one obtains a fixed point. The same techniques apply to homeomorphisms of the torus T2. In this setting we show that if f is homotopic to the identity, preserves Lebesgue measure and has mean translation 0, then it has at least one fixed point.

scholarly journals Fixed Points and the Stability of an AQCQ-Functional Equation in Non-Archimedean Normed Spaces

2010 ◽  
Vol 2010 ◽  
pp. 1-15 ◽  
Author(s):  
Choonkil Park
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Fixed Points ◽  
Banach Spaces ◽  
Fixed Point Method ◽  
Point Method ◽  
Ulam Stability ◽  
Normed Spaces ◽  
Quartic Functional Equation ◽  
The Stability

Using fixed point method, we prove the generalized Hyers-Ulam stability of the following additive-quadratic-cubic-quartic functional equationf(x+2y)+f(x−2y)=4f(x+y)+4f(x−y)−6f(x)+f(2y)+f(−2y)−4f(y)−4f(−y)in non-Archimedean Banach spaces.

scholarly journals TARGET SPACE DUALITY AND MODULI STABILIZATION IN STRING GAS COSMOLOGY

2007 ◽  
Vol 22 (01) ◽  
pp. 165-179 ◽  
Author(s):  
AUTTAKIT CHATRABHUTI
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Moduli Space ◽  
Target Space ◽  
Moduli Stabilization ◽  
String Gas Cosmology ◽  
The Stability

Motivated by string gas cosmology, we investigate the stability of moduli fields coming from compactifications of string gas on torus with background flux. It was previously claimed that moduli are stabilized only at a single fixed-point in moduli space, a self-dual point of T-duality with vanishing flux. Here, we show that there exist other stable fixed-points on moduli space with nonvanishing flux. We also discuss the more general target space dualities associated with these fixed-points.

scholarly journals Stability to a Kind of Functional Differential Equations of Second Order with Multiple Delays by Fixed Points

2014 ◽  
Vol 2014 ◽  
pp. 1-9
Author(s):  
Cemil Tunç ◽  
Emel Biçer
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Functional Differential Equations ◽  
Multiple Delays ◽  
Stability Of Solutions ◽  
Variable Delays ◽  
Multiple Variable ◽  
Fixed Point Technique ◽  
Functional Differential ◽  
The Stability

We discuss the stability of solutions to a kind of scalar Liénard type equations with multiple variable delays by means of the fixed point technique under an exponentially weighted metric. By this work, we improve some related results from one delay to multiple variable delays.

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