On critical point for two-dimensional holomorphic systems

2016 ◽  
Vol 37 (7) ◽  
pp. 2276-2312
Author(s):  
FRANCISCO VALENZUELA-HENRÍQUEZ
Keyword(s):  
Critical Point ◽  
Complex Manifold ◽  
Invariant Set ◽  
Two Dimensional ◽  
Dominated Splitting ◽  
One Dimensional ◽  
Dynamical Object ◽  
Dynamical Properties

Let $f:M\rightarrow M$ be a biholomorphism on a two-dimensional complex manifold, and let $X\subseteq M$ be a compact $f$-invariant set such that $f|_{X}$ is asymptotically dissipative and without periodic sinks. We introduce a solely dynamical obstruction to dominated splitting, namely critical point. Critical point is a dynamical object and captures many of the dynamical properties of a one-dimensional critical point.

SOME PECULIAR PROPERTIES OF THE DARWIN’S LAGRANGIAN

1995 ◽  
Vol 09 (23) ◽  
pp. 3069-3083 ◽  
Author(s):  
I.P. PAVLOTSKY ◽  
M. STRIANESE
Keyword(s):  
Phase Space ◽  
Dimensional Case ◽  
Minimal Distance ◽  
Rectilinear Motion ◽  
Two Dimensional ◽  
Singular Surfaces ◽  
One Dimensional ◽  
Local Singularity ◽  
Dynamical Properties

In the post-Galilean approximation the Lagrangians are singular on a submanifold of the phase space. It is a local singularity, which differs from the ones considered by Dirac. The dynamical properties are essentially peculiar on the studied singular surfaces. In the preceding publications,1,2,3 two models of singular relativistic Lagrangians and the rectilinear motion of two electrons, determined by Darwin’s Lagrangian, were examined. In the present paper we study the peculiar dynamical properties of the two-dimensional Darwin’s Lagrangian. In particular, it is shown that the minimal distance between two electrons (the so called “radius of electron”) appears in the two-dimensional motion as well as in one-dimensional case. Some new peculiar properties are discovered.

scholarly journals On the notion of the dimension with respect to a dynamical system

1984 ◽  
Vol 4 (3) ◽  
pp. 405-420 ◽  
Author(s):  
Ya. B. Pesin
Keyword(s):  
Dynamical System ◽  
Hausdorff Dimension ◽  
Invariant Sets ◽  
Dimensional Case ◽  
Two Dimensional ◽  
One Dimensional ◽  
Common Features ◽  
Dynamical Properties ◽  
The One ◽  
Hyperbolic Sets

AbstractFor the invariant sets of dynamical systems a new notion of dimension-the so-called dimension with respect to a dynamical system-is introduced. It has some common features with the general topological notion of the dimension, but it also reflects the dynamical properties of the system. In the one-dimensional case it coincides with the Hausdorff dimension. For multi-dimensional hyperbolic sets formulae for the calculation of our dimension are obtained. These results are generalizations of Manning's results obtained by him for the Hausdorff dimension in the two-dimensional case.

ON BEHAVIORS OF TWO-DIMENSIONAL ENDOMORPHISMS: ROLE OF THE CRITICAL CURVES

1993 ◽  
Vol 03 (01) ◽  
pp. 187-194 ◽  
Author(s):  
CHRISTIAN MIRA ◽  
TONY NARAYANINSAMY
Keyword(s):  
Critical Points ◽  
Two Dimensional ◽  
One Dimensional ◽  
Critical Curves ◽  
Dynamical Properties

Critical curves are the natural two-dimensional extension of the notion of critical points in one-dimensional endomorphisms. They play a fundamental role in determining the dynamical properties and their bifurcations. This letter demonstrates such a role for two new behaviors.

ESTIMATING THE DIMENSIONAL CHARACTERISTICS OF TWO-DIMENSIONAL PATTERNS

1995 ◽  
Vol 05 (01) ◽  
pp. 109-121 ◽  
Author(s):  
A.L. ZHELEZNYAK ◽  
L.O. CHUA
Keyword(s):  
Fractal Dimensions ◽  
Computer Experiments ◽  
Two Dimensional ◽  
One Dimensional ◽  
Theoretical Predictions ◽  
The Matrix ◽  
Spatially Extended ◽  
Spatially Extended Systems ◽  
Dynamical Properties ◽  
Generalized Dimensions

Dynamical properties of two-dimensional patterns generated by spatially extended systems can be described via the characteristics of attractors in the matrix phase space of the associated translation (or translational-evolution) dynamical systems. Questions regarding the possibility of estimating the fractal dimensions of two-dimensional patterns from the fractal dimensions of one-dimensional observables scanning the patterns along a chosen path are investigated. The presented proofs state that the generalized dimensions of the scanning observables are lower bounds for estimating the corresponding generalized dimensions of two-dimensional patterns. Spatial field distributions defined as superposition of planar waves and different spatiotemporal patterns produced by cellular neural networks made of Chua’s circuits are studied numerically. The results of computer experiments confirm the theoretical predictions presented in this paper.

Structure and dynamical properties of two-dimensional dusty plasmas on one-dimensional periodic substrates

2021 ◽  
Vol 28 (4) ◽  
pp. 040501
Author(s):  
Yan Feng ◽  
Wei Li ◽  
C. Reichhardt ◽  
C. J. O. Reichhardt ◽  
M. S. Murillo
Keyword(s):  
Dusty Plasmas ◽  
Two Dimensional ◽  
One Dimensional ◽  
Dynamical Properties

Interplay between water adsorption and viscosity determines the spatial configuration of EPS during soil drying

2020 ◽  
Author(s):  
Andrea Carminati ◽  
Pascal Benard ◽  
Judith Schepers ◽  
Margherita Crosta ◽  
Mohsen Zarebanadkouki
Keyword(s):  
Surface Tension ◽  
Critical Point ◽  
Extracellular Polymeric Substances ◽  
Water Adsorption ◽  
Spatial Configuration ◽  
Solid Surfaces ◽  
Two Dimensional ◽  
Soil Matrix ◽  
One Dimensional ◽  
Drying Rates

<p>Bacteria alter the physical properties of soil hotspots by secreting extracellular polymeric substances EPS. Despite the biogeochemical importance of these alterations is well accepted, the physical mechanisms by which EPS shapes the properties of the soil solution and its interactions with the soil matrix are not well understood.</p><p>Here we show that upon drying in porous media EPS forms one-dimensional filaments and two-dimensional interconnected structures spanning across multiple pores. Unlike water, primarily shaped by surface tension, EPS remains connected upon drying thanks to its high extensional viscosity. The integrity of one-dimensional structures is explained by the interplay of viscosity and surface tension forces (characterized by the Ohnesorge number), while the formation of two-dimensional structures requires consideration of the interaction of EPS with the solid surfaces and external drivers, such as the drying rate. During drying, the viscosity of EPS increases and, at a critical point, when the friction between polymers and solid surfaces overcomes the water adsorption of the polymers, the concentration of the polymer solution at the liquid-gas interface increases asymptotically and the polymers can no longer follow the retreating gas-water interface. At this critical point the polymers do not move any longer and are deposited as two-dimensional surfaces, such as hollow cylinders or interconnected surfaces. EPS viscosity, specific soil surface and drying rates are the key parameters determining the transition from one- to two-dimensional structures.</p><p>The high viscosity of EPS maintains the connectivity of the liquid phase during drying in soil hotspots, such as bacterial colonies, the rhizosphere and biological soil crusts.</p>

scholarly journals Scaling Properties of a Hybrid Fermi-Ulam-Bouncer Model

2009 ◽  
Vol 2009 ◽  
pp. 1-13 ◽  
Author(s):  
Diego F. M. Oliveira ◽  
Rafael A. Bizão ◽  
Edson D. Leonel
Keyword(s):  
Critical Exponents ◽  
Average Velocity ◽  
Chaotic Regime ◽  
Two Dimensional ◽  
Scaling Properties ◽  
One Dimensional ◽  
Dynamical Properties ◽  
Scaling Invariant ◽  
Area Preserving

Some dynamical properties for a one-dimensional hybrid Fermi-Ulam-bouncer model are studied under the framework of scaling description. The model is described by using a two-dimensional nonlinear area preserving mapping. Our results show that the chaotic regime below the lowest energy invariant spanning curve is scaling invariant and the obtained critical exponents are used to find a universal plot for the second momenta of the average velocity.

A one-dimensional self-gravitating stellar gas

1966 ◽  
Vol 25 ◽  
pp. 46-48 ◽  
Author(s):  
M. Lecar
Keyword(s):  
Gravitational Field ◽  
Phase Space ◽  
Motion Picture ◽  
Space Distribution ◽  
Two Dimensional ◽  
One Dimensional ◽  
Phase Space Distribution ◽  
Dimensional Phase Space ◽  
The Mean

“Dynamical mixing”, i.e. relaxation of a stellar phase space distribution through interaction with the mean gravitational field, is numerically investigated for a one-dimensional self-gravitating stellar gas. Qualitative results are presented in the form of a motion picture of the flow of phase points (representing homogeneous slabs of stars) in two-dimensional phase space.

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