Nontwist systems, common in the dynamical descriptions of fluids and plasmas, possess a shearless curve with a concomitant transport barrier that eliminates or reduces chaotic transport, even after its breakdown. In order to investigate the transport properties of nontwist systems, we analyze the barrier escape time and barrier transmissivity for the standard nontwist map, a paradigm of such systems. We interpret the sensitive dependence of these quantities upon map parameters by investigating chaotic orbit stickiness and the associated role played by the dominant crossing of stable and unstable manifolds.

1.
J.
Moser
,
Ergod. Theory Dyn. Syst.
6
,
401
(
1986
).
2.
A. N.
Lichtenberg
and
M. A.
Lieberman
,
Regular and Chaotic Dynamics
, 2nd ed. (
Springer Verlag
,
Berlin
,
1992
).
3.
B. V.
Chirikov
,
Phys. Rep.
52
,
263
(
1979
).
4.
D.
Del-Castillo-Negrete
and
P. J.
Morrison
,
Phys. Fluids A
5
,
948
(
1993
).
5.
D.
Del-Castillo-Negrete
,
J. M.
Greene
, and
P. J.
Morrison
,
Physica D
91
,
1
(
1996
).
6.
D.
Del-Castillo-Negrete
,
J. M.
Greene
, and
P. J.
Morrison
,
Physica D
100
,
311
(
1997
).
7.
D.
Del-Castillo-Negrete
and
P. J.
Morrison
, in
Chaotic Dynamics and Transport in Fluids and Plasmas
,
Research Trends in Physics
, edited by
I.
Prigogine
(
American Institute of Physics
,
New York
,
1992
), p.
181
.
8.
W.
Kerner
and
H.
Tasso
,
Phys. Rev. Lett.
49
,
654
(
1982
).
9.
M. G.
Davidson
,
R. L.
Dewar
,
H. J.
Gardner
, and
J.
Howard
,
Aust. J. Phys.
48
,
871
(
1995
).
10.
M. P.
Bernardin
and
J. A.
Tataronis
,
J. Math. Phys.
26
,
2370
(
1985
).
11.
P. J.
Morrison
,
Rev. Mod. Phys.
70
,
467
(
1998
);
P. J.
Morrison
,
Phys. Plasmas
7
,
2279
(
2000
).
12.
E.
Mazzucato
,
S. H.
Batha
,
M.
Beer
,
M.
Bell
,
R. E.
Bell
,
R. V.
Budny
,
C.
Bush
,
T. S.
Hahm
,
G. W.
Hammett
,
F. M.
Levinton
,
R.
Nazikian
,
H.
Park
,
G.
Rewoldt
,
G. L.
Schmidt
,
E. J.
Synakowski
,
W. M.
Tang
,
G.
Taylor
, and
M. C.
Zarnstorff
,
Phys. Rev. Lett.
77
,
3145
(
1996
).
13.
D.
Del-Castillo-Negrete
and
P. J.
Morrison
,
Bull. Am. Phys. Soc.
37
,
1547
(
1992
).
14.
W.
Horton
,
H. B.
Park
,
J. M.
Kwon
,
D.
Strozzi
,
P. J.
Morrison
, and
D. I.
Choi
,
Phys. Plasmas
5
,
3910
(
1998
).
15.
E. C.
da Silva
,
I. L.
Caldas
, and
R. L.
Viana
,
IEEE Trans. Plasma Sci.
29
,
617
(
2001
).
16.
G. A.
Oda
and
I. L.
Caldas
,
Chaos, Solitons Fractals
5
,
15
(
1995
);
G.
Corso
and
A. J.
Lichtenberg
,
Physica D
131
,
1
(
1999
).
17.
D.
Del-Castillo-Negrete
,
Phys. Plasmas
7
,
1702
(
2000
).
18.
F. A.
Marcus
,
T.
Kroetz
,
M.
Roberto
,
I. L.
Caldas
,
E. C.
da Silva
,
R. L.
Viana
, and
Z. O.
Guimarães-Filho
,
Nucl. Fusion
48
,
024108
(
2008
).
19.
F. A.
Marcus
,
I. L.
Caldas
,
Z. O.
Guimarães-Filho
,
P. J.
Morrison
,
W.
Horton
,
Yu. K.
Kuznetsov
, and
I. C.
Nascimento
,
Phys. Plasmas
15
,
112304
(
2008
).
20.
M.
Jakubowski
,
S. S.
Abdullaev
,
K. H.
Finken
,
M.
Lehnen
, and the
TEXTOR Team
,
J. Nucl. Mater.
532
,
337
(
2005
).
21.
A.
Wingen
,
M.
Jakubowski
,
K. H.
Spatschek
,
S. S.
Abdullaev
,
K. H.
Finken
, and
A.
Lehnen
,
Phys. Plasmas
14
,
042502
(
2007
).
22.
T. E.
Evans
,
I.
Joseph
,
R. A.
Moyer
,
M. E.
Fenstermacher
,
C. J.
Lasnler
, and
L. W.
Yan
,
J. Nucl. Mater.
363–365
,
570
(
2007
).
23.
A.
Wurm
,
A.
Apte
, and
P. J.
Morrison
,
Braz. J. Phys.
34
,
1700
(
2004
).
24.
A.
Wurm
,
A.
Apte
,
K.
Fuchss
, and
P. J.
Morrison
,
Chaos
15
,
023108
(
2005
).
25.
S.
Aubry
and
P. Y.
LeDaeron
,
Physica D
8
,
381
(
1983
);
J. N.
Mather
,
Topology
21
,
457
(
1982
);
R. S.
MacKay
,
Nonlinearity
5
,
161
(
1992
).
26.
A.
Delshams
and
R.
de la Llave
,
SIAM J. Math. Anal.
31
,
1235
(
2000
).
27.
C.
Simo
,
Regular Chaotic Dyn.
3
,
180
(
1998
).
28.
H. R.
Dullin
,
J. D.
Meiss
, and
D.
Sterling
,
Nonlinearity
13
,
203
(
2000
).
29.
K.
Ullmann
and
I. L.
Caldas
,
Chaos, Solitons Fractals
11
,
2129
(
2000
).
30.
J. D.
Meiss
and
E.
Ott
,
Phys. Rev. Lett.
55
,
2741
(
1985
);
[PubMed]
G.
Zaslavsky
and
M.
Edelman
,
Chaos
10
,
135
(
2000
).
[PubMed]
31.
D.
Del-Castillo-Negrete
,
B. A.
Carreras
, and
V. E.
Lynch
,
Phys. Plasmas
11
,
3854
(
2004
).
32.
J. D.
Szezech
, Jr.
,
S. R.
Lopes
, and
R. L.
Viana
,
Phys. Lett. A
335
,
394
(
2005
).
33.
E.
Ott
,
Chaos in Dynamical Systems
(
Cambridge University Press
,
Cambridge, England
,
1993
).
34.
G.
Corso
and
F. B.
Rizzato
,
Phys. Rev. E
58
,
8013
(
1998
).
35.
T. E.
Evans
,
R. A.
Moyer
, and
P.
Monat
,
Phys. Plasmas
9
,
4957
(
2002
).
36.
H.
Kantz
and
P.
Grassberger
,
Physica D
17
,
75
(
1985
).
37.
J. S. E.
Portela
,
I. L.
Caldas
,
R. L.
Viana
, and
M. A. F.
Sanjuán
,
Int. J. Bifurcation Chaos Appl. Sci. Eng.
17
,
4067
(
2007
).
38.
R. S.
MacKay
,
J. D.
Meiss
, and
I. C.
Percival
,
Physica D
13
,
55
(
1984
).
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