Non isolated periodic orbits of a fixed period for quadratic dynamical systems

2018 ◽  
Vol 12 (22) ◽  
pp. 1053-1058
Author(s):  
Hamza Boujemaa ◽  
Said El Qotbi
Keyword(s):  
Dynamical Systems ◽  
Periodic Orbits ◽  
Fixed Period

scholarly journals About the Orbit Structure of Sequences of Maps of Integers

Symmetry ◽  
2019 ◽  
Vol 11 (11) ◽  
pp. 1374
Author(s):  
Viorel Niţică ◽  
Jeroz Makhania
Keyword(s):  
Dynamical Systems ◽  
Periodic Orbits ◽  
Point Of View ◽  
Orbit Structure ◽  
Unbounded Orbits ◽  
Fixed Period

Motivated by connections to the study of sequences of integers, we study, from a dynamical systems point of view, the orbit structure for certain sequences of maps of integers. We find sequences of maps for which all individual orbits are bounded and periodic and for which the number of periodic orbits of fixed period is finite. This allows the introduction of a formal ζ -function for the maps in these sequences, which are actually polynomials. We also find sequences of maps for which the orbit structure is more complicated, as they have both bounded and unbounded orbits, both individual and global. Most of our results are valid in a general numeration base.

scholarly journals Numerical detection of unstable periodic orbits in continuous-time dynamical systems with chaotic behaviors

2007 ◽  
Vol 14 (5) ◽  
pp. 615-620 ◽  
Author(s):  
Y. Saiki
Keyword(s):  
Dynamical Systems ◽  
Periodic Orbits ◽  
Infinite Number ◽  
Continuous Time ◽  
Chaotic Systems ◽  
Lorenz System ◽  
Complex Phenomenon ◽  
Unstable Periodic Orbits ◽  
Newton Raphson ◽  
The Lorenz System

Abstract. An infinite number of unstable periodic orbits (UPOs) are embedded in a chaotic system which models some complex phenomenon. Several algorithms which extract UPOs numerically from continuous-time chaotic systems have been proposed. In this article the damped Newton-Raphson-Mees algorithm is reviewed, and some important techniques and remarks concerning the practical numerical computations are exemplified by employing the Lorenz system.

scholarly journals On the Periodic Structure of Parallel Dynamical Systems on Generalized Independent Boolean Functions

Mathematics ◽  
2020 ◽  
Vol 8 (7) ◽  
pp. 1088 ◽  
Author(s):  
Juan A. Aledo ◽  
Ali Barzanouni ◽  
Ghazaleh Malekbala ◽  
Leila Sharifan ◽  
Jose C. Valverde
Keyword(s):  
Fixed Point ◽  
Dynamical Systems ◽  
Periodic Orbits ◽  
Periodic Structure ◽  
Boolean Functions ◽  
Directed Graphs ◽  
General Pattern ◽  
General Situation ◽  
Point System ◽  
Local Functions

In this paper, based on previous results on AND-OR parallel dynamical systems over directed graphs, we give a more general pattern of local functions that also provides fixed point systems. Moreover, by considering independent sets, this pattern is also generalized to get systems in which periodic orbits are only fixed points or 2-periodic orbits. The results obtained are also applicable to homogeneous systems. On the other hand, we study the periodic structure of parallel dynamical systems given by the composition of two parallel systems, which are conjugate under an invertible map in which the inverse is equal to the original map. This allows us to prove that the composition of any parallel system on a maxterm (or minterm) Boolean function and its conjugate one by means of the complement map is a fixed point system, when the associated graph is undirected. However, when the associated graph is directed, we demonstrate that the corresponding composition may have points of any period, even if we restrict ourselves to the simplest maxterm OR and the simplest minterm AND. In spite of this general situation, we prove that, when the associated digraph is acyclic, the composition of OR and AND is a fixed point system.

scholarly journals Periodic Orbits of Third Kind in the Zonal J2 + J3 Problem

Symmetry ◽  
2019 ◽  
Vol 11 (1) ◽  
pp. 111
Author(s):  
M. de Bustos ◽  
Antonio Fernández ◽  
Miguel López ◽  
Raquel Martínez ◽  
Juan Vera
Keyword(s):  
Dynamical Systems ◽  
Phase Portrait ◽  
Periodic Orbits ◽  
Averaging Theory ◽  
The Third ◽  
Explicit Expressions

In this work, the periodic orbits’ phase portrait of the zonal J 2 + J 3 problem is studied. In particular, we center our attention on the periodic orbits of the third kind in the Poincaré sense using the averaging theory of dynamical systems. We find three families of polar periodic orbits and four families of inclined periodic orbits for which we are able to state their explicit expressions.

scholarly journals Periodic Orbits and Subharmonics of Dynamical Systems on Non-Compact Riemannian Manifolds

1996 ◽  
Vol 130 (1) ◽  
pp. 142-161 ◽  
Author(s):  
Silvia Cingolani ◽  
Elvira Mirenghi ◽  
Maria Tucci
Keyword(s):  
Dynamical Systems ◽  
Periodic Orbits ◽  
Riemannian Manifolds
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