Closed orbits and the hyperspace of 12-homogeneous continua

2021 ◽  
Vol 289 ◽  
pp. 107456
Author(s):  
Norberto Ordoñez ◽  
César Piceno ◽  
Hugo Villanueva
Keyword(s):  
Closed Orbits

scholarly journals A new catalogue of multiple galaxies in the Local Supercluster

2000 ◽  
Vol 174 ◽  
pp. 40-45
Author(s):  
D. I. Makarov ◽  
I. D. Karachentsev
Keyword(s):  
New Approach ◽  
Galaxy Groups ◽  
Closed Orbits ◽  
Crossing Time ◽  
Local Supercluster ◽  
Virial Mass ◽  
Nearby Galaxies ◽  
The Individual ◽  
Group Member ◽  
Harmonic Radius

AbstractA new approach is suggested which makes use of the individual properties of galaxies, for the identification of small galaxy groups in the Local Supercluster. The criterion is based on the assumption of closed orbits of the companions around the dominating group member within a zero velocity sphere.The criterion is applied to a sample of 6321 nearby galaxies with radial velocities V0 ≤ 3000 km s−1. These 3472 galaxies have been assigned to 839 groups that include 55% of the sample considered. For the groups identified by the new algorithm (with k ≥ 5 members) the median velocity dispersion is 86 km s−1, the median harmonic radius is 247 kpc, the median crossing time is 0.08(1/H), and the median virial-mass-to-light ratio is 56 M⊙/L⊙.

scholarly journals Multiple closed orbits for N-body-type problems

1998 ◽  
Vol 58 (1) ◽  
pp. 1-13 ◽  
Author(s):  
Shiqing Zhang
Keyword(s):  
Lower Bound ◽  
Periodic Solutions ◽  
Upper Bound ◽  
Critical Value ◽  
Body Type ◽  
Fixed Energy ◽  
Closed Orbits

Using the equivariant Ljusternik-Schnirelmann theory and the estimate of the upper bound of the critical value and lower bound for the collision solutions, we obtain some new results in the large concerning multiple geometrically distinct periodic solutions of fixed energy for a class of planar N-body type problems.

Resonances and Torsion Numbers of Driven Dissipative Nonlinear Oscillators

1986 ◽  
Vol 41 (4) ◽  
pp. 605-614 ◽  
Author(s):  
Ulrich Parlitz ◽  
Werner Lauterborn
Keyword(s):  
Nonlinear Oscillators ◽  
Winding Number ◽  
Local Flow ◽  
One Dimensional ◽  
Bifurcation Set ◽  
Local Bifurcations ◽  
Closed Orbits

The torsion of the local flow around closed orbits and its relation to the superstructure in the bifurcation set of strictly dissipative nonlinear oscillators is investigated. The torsion number describing the twisting behaviour of the flow turns out to be a suitable invariant for the classification of local bifurcations and resonances in those systems. Furthermore, the notions of winding number and resonance are generalized to arbitrary one-dimensional dissipative oscillators.

scholarly journals Symbolic dynamics for non-uniformly hyperbolic systems

2020 ◽  
pp. 1-68
Author(s):  
YURI LIMA
Keyword(s):  
Symbolic Dynamics ◽  
Hyperbolic Systems ◽  
Markov Partition ◽  
Equilibrium Measures ◽  
Markov Partitions ◽  
Recent Advances ◽  
Closed Orbits ◽  
Symbolic Extension ◽  
Uniformly Hyperbolic Systems

Abstract This survey describes the recent advances in the construction of Markov partitions for non-uniformly hyperbolic systems. One important feature of this development comes from a finer theory of non-uniformly hyperbolic systems, which we also describe. The Markov partition defines a symbolic extension that is finite-to-one and onto a non-uniformly hyperbolic locus, and this provides dynamical and statistical consequences such as estimates on the number of closed orbits and properties of equilibrium measures. The class of systems includes diffeomorphisms, flows, and maps with singularities.

scholarly journals Global Analysis of a Liénard System with Quadratic Damping

2018 ◽  
Vol 2018 ◽  
pp. 1-9
Author(s):  
Feng Guo
Keyword(s):  
Necessary Conditions ◽  
Global Analysis ◽  
Global Bifurcation ◽  
Phase Portraits ◽  
Liénard System ◽  
Closed Orbits ◽  
Lienard System ◽  
Sufficient And Necessary Conditions ◽  
Global Phase Portrait ◽  
Quadratic Damping

In this paper, the global analysis of a Liénard equation with quadratic damping is studied. There are 22 different global phase portraits in the Poincaré disc. Every global phase portrait is given as well as the complete global bifurcation diagram. Firstly, the equilibria at finite and infinite of the Liénard system are discussed. The properties of the equilibria are studied. Then, the sufficient and necessary conditions of the system with closed orbits are obtained. The degenerate Bogdanov-Takens bifurcation is studied and the bifurcation diagrams of the system are given.

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