scholarly journals Minimal topological chaos coexisting with a finite set of homoclinic and periodic orbits

2016 ◽  
Vol 315 ◽  
pp. 83-89 ◽  
Author(s):  
Walter Huaraca ◽  
Valentín Mendoza
Keyword(s):  
Periodic Orbits ◽  
Topological Chaos ◽  
Finite Set

Lefschetz numbers of periodic orbits of pseudo-Anosov homeomorphisms

1994 ◽  
Vol 115 (1) ◽  
pp. 121-132 ◽  
Author(s):  
John Guaschi
Keyword(s):  
Periodic Orbit ◽  
Periodic Orbits ◽  
Periodic Points ◽  
Lefschetz Numbers ◽  
Finite Set ◽  
Surface Homeomorphism

AbstractGiven a surface homeomorphism isotopic to the identity which is pseudo-Anosov relative to a finite set, we show that the sum of the Lefschetz numbers of periodic points of any period greater than one is non-negative. If this period is odd and greater than a number which depends only on the surface, the sum is zero. If we consider sequences of periods such that each element is twice that of its predecessor, then this sum is increasing beyond a certain point also depending on the surface. As a corollary, for each periodic orbit contained within the boundary of the surface there exists one of the same period contained in the interior.

Asymptotic entropy, periodic orbits, and pseudo-Anosov maps

1998 ◽  
Vol 18 (2) ◽  
pp. 425-439 ◽  
Author(s):  
JAROSLAW KWAPISZ ◽  
RICHARD SWANSON
Keyword(s):  
Periodic Orbits ◽  
Rotation Numbers ◽  
Finite Set ◽  
Asymptotic Entropy

In this paper we derive some properties of a variety of entropy that measures rotational complexity of annulus homeomorphisms, called asymptotic or rotational entropy. In previous work [KS] the authors showed that positive asymptotic entropy implies the existence of infinitely many periodic orbits corresponding to an interval of rotation numbers. In our main result, we show that a Hölder $C^1$ diffeomorphism with nonvanishing asymptotic entropy is isotopic rel a finite set to a pseudo-Anosov map. We also prove that the closure of the set of recurrent points supports positive asymptotic entropy for a ($C^0$) homeomorphism with nonzero asymptotic entropy.

Adaptive Control of Transient Dynamics to Periodic Orbits

2014 ◽  
Vol 2 ◽  
pp. 82-85
Author(s):  
Hiroyasu Ando ◽  
Kazuyuki Aihara
Keyword(s):  
Adaptive Control ◽  
Periodic Orbits ◽  
Transient Dynamics

Non-repetitive sequences

1970 ◽  
Vol 68 (2) ◽  
pp. 267-274 ◽  
Author(s):  
P. A. B. Pleasants
Keyword(s):  
Repetitive Sequences ◽  
Finite Set ◽  
Infinite Sequences

This note is concerned with infinite sequences whose terms are chosen from a finite set of symbols. A segment of such a sequence is a set of one or more consecutive terms, and a repetition is a pair of finite segments that are adjacent and identical. A non-repetitive sequence is one that contains no repetitions.

The inverse problem of recovering the coefficients of a differential equations on a graph

2020 ◽  
Vol 28 (5) ◽  
pp. 727-738
Author(s):  
Victor Sadovnichii ◽  
Yaudat Talgatovich Sultanaev ◽  
Azamat Akhtyamov
Keyword(s):  
Inverse Problem ◽  
Inverse Problems ◽  
Differential Equations ◽  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Finite Number ◽  
Characteristic Equation ◽  
Arbitrary Number ◽  
New Class ◽  
Finite Set

AbstractWe consider a new class of inverse problems on the recovery of the coefficients of differential equations from a finite set of eigenvalues of a boundary value problem with unseparated boundary conditions. A finite number of eigenvalues is possible only for problems in which the roots of the characteristic equation are multiple. The article describes solutions to such a problem for equations of the second, third, and fourth orders on a graph with three, four, and five edges. The inverse problem with an arbitrary number of edges is solved similarly.

scholarly journals A Novel Simplified Implementation of Finite-Set Model Predictive Control for Power Converters

IEEE Access ◽  
2021 ◽  
pp. 1-1
Author(s):  
Jose J. Silva ◽  
Jose R. Espinoza ◽  
Jaime A. Rohten ◽  
Esteban S. Pulido ◽  
Felipe A. Villarroel ◽  
...  
Keyword(s):  
Model Predictive Control ◽  
Predictive Control ◽  
Power Converters ◽  
Finite Set
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