Periodic and Quasi-Periodic Orbits for Twist Maps

2020 ◽  
pp. 376-394
Author(s):  
A. Katok
Keyword(s):  
Periodic Orbits ◽  
Twist Maps

scholarly journals Birkhoff periodic orbits for twist maps with the graph intersection property

1985 ◽  
Vol 5 (4) ◽  
pp. 531-537 ◽  
Author(s):  
David Bernstein
Keyword(s):  
Periodic Orbits ◽  
Intersection Property ◽  
Twist Maps

AbstractIn this paper we show that Birkhoff periodic orbits actually exist for arbitrary monotone twist maps satisfying the graph intersection property.

Rotationally-ordered periodic orbits for multiharmonic area-preserving twist maps

1994 ◽  
Vol 73 (4) ◽  
pp. 388-398 ◽  
Author(s):  
J.A. Ketoja ◽  
R.S. MacKay
Keyword(s):  
Periodic Orbits ◽  
Twist Maps ◽  
Area Preserving

Denjoy minimal sets and Birkhoff periodic orbits for non-exact monotone twist maps

2018 ◽  
Vol 264 (11) ◽  
pp. 7006-7021
Author(s):  
Wen-Xin Qin ◽  
Ya-Nan Wang
Keyword(s):  
Periodic Orbits ◽  
Minimal Sets ◽  
Twist Maps

scholarly journals On the existence of a new type of periodic and quasi-periodic orbits for twist maps of the torus

Nonlinearity ◽  
2002 ◽  
Vol 15 (5) ◽  
pp. 1399-1416 ◽  
Author(s):  
Salvador Addas-Zanata
Keyword(s):  
Periodic Orbits ◽  
Twist Maps ◽  
New Type

ELLIPTIC NON-BIRKHOFF PERIODIC ORBITS IN THE TWIST MAPS

1993 ◽  
Vol 03 (01) ◽  
pp. 165-185 ◽  
Author(s):  
ARTURO OLVERA ◽  
CARLES SIMÓ
Keyword(s):  
Periodic Orbits ◽  
Periodic Points ◽  
Irrational Rotation ◽  
Point Of View ◽  
Twist Map ◽  
Qualitative And Quantitative ◽  
Open Set ◽  
Twist Maps ◽  
Rotational Curve ◽  
Irrational Rotation Number

We consider a perturbed twist map when the perturbation is big enough to destroy the invariant rotational curve (IRC) with a given irrational rotation number. Then an invariant Cantorian set appears. From another point of view, the destruction of the IRC is associated with the appearance of heteroclinic connections between hyperbolic periodic points. Furthermore the destruction of the IRC is also associated with the existence of non-Birkhoff orbits. In this paper we relate the different approaches. In order to explain the creation of non-Birkhoff orbits, we provide qualitative and quantitative models. We show the existence of elliptic non-Birkhoff periodic orbits for an open set of values of the perturbative parameter. The bifurcations giving rise to the elliptic non-Birkhoff orbits and other related bifurcations are analysed. In the last section, we show a celestial mechanics example displaying the described behavior.

scholarly journals Periodic orbits for dissipative twist maps

1987 ◽  
Vol 7 (2) ◽  
pp. 165-173 ◽  
Author(s):  
Martin Casdagli
Keyword(s):  
Variational Methods ◽  
Periodic Orbits ◽  
Twist Maps ◽  
Dissipative Case ◽  
Area Preserving

AbstractWe develop simple topological criteria for the existence of periodic orbits in maps of the annulus. These are applied to one-parameter families of dissipative twist maps of the annulus and their attractors. It follows that many of the motions found by variational methods in area preserving twist maps also occur in the dissipative case.

scholarly journals The birth process of periodic orbits in non-twist maps

1990 ◽  
Vol 169 (1) ◽  
pp. 42-72 ◽  
Author(s):  
J.P. Van der Weele ◽  
T.P. Valkering
Keyword(s):  
Periodic Orbits ◽  
Birth Process ◽  
Twist Maps

scholarly journals Invariant circles and the order structure of periodic orbits in monotone twist maps

Topology ◽  
1987 ◽  
Vol 26 (1) ◽  
pp. 21-35 ◽  
Author(s):  
Philip L. Boyland ◽  
Glen Richard Hall
Keyword(s):  
Periodic Orbits ◽  
Order Structure ◽  
Invariant Circles ◽  
Twist Maps
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