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Physica D: Nonlinear Phenomena, ISSN 0167-2789, 07/2015, Volume 308, pp. 34 - 39
Abstract We numerically explore Slater's theorem in the context of dynamical systems to study the breakup of invariant curves. Slater's theorem states that an... 
Twist maps | Slater's theorem | Nontwist maps | Invariant curves | MATHEMATICS, APPLIED | PHYSICS, MULTIDISCIPLINARY | PHYSICS, FLUIDS & PLASMAS | PHYSICS, MATHEMATICAL | NONTWIST | MAPS | TORI | CIRCLES | KAM | MEANDERS | RENORMALIZATION
Journal Article
Physica D: Nonlinear Phenomena, ISSN 0167-2789, 07/2015, Volume 308, pp. 34 - 39
We numerically explore Slater’s theorem in the context of dynamical systems to study the breakup of invariant curves. Slater’s theorem states that an... 
Twist maps | Nontwist maps | Slater’s theorem | Invariant curves
Journal Article
Physica A: Statistical Mechanics and its Applications, ISSN 0378-4371, 12/2015, Volume 440, pp. 42 - 48
We present a new kind of one-dimensional attractor, which has not yet been predicted in the non-linear dynamics theory. We consider a non-linear map, which... 
Shrimps | New attractor | Shearless | Indicator points | Non-twist map | NONTWIST | TRANSITION | TRANSPORT | MAPS | PHYSICS, MULTIDISCIPLINARY | RECONNECTION
Journal Article
Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, ISSN 1539-3755, 06/2013, Volume 87, Issue 6, p. 063106
A study of anisotropic heat transport in reversed shear (nonmonotonic q-profile) magnetic fields is presented. The approach is based on a recently proposed... 
TRANSITION | PERIODIC-ORBITS | CHAOS | PHYSICS, FLUIDS & PLASMAS | HAMILTONIAN-SYSTEMS | RECONNECTION | PRESERVING NONTWIST MAPS | PHYSICS, MATHEMATICAL | LINES
Journal Article
Chaos, Solitons and Fractals: the interdisciplinary journal of Nonlinear Science, and Nonequilibrium and Complex Phenomena, ISSN 0960-0779, 10/2016, Volume 91, pp. 128 - 135
The aim of the paper is to study systems with one-and-a-half degrees of freedom generated by a Hamiltonian with a quartic unperturbed part and broad... 
Hamiltonian systems | Reconnection bifurcation | Nontwist maps | MAGNETIC-FIELD LINES | PHYSICS, MULTIDISCIPLINARY | TRANSPORT BARRIERS | RECONNECTION | MODEL | PHYSICS, MATHEMATICAL | TRANSITION | CHAOS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | SYMMETRY | STOCHASTICITY | DYNAMICS | TOKAMAK
Journal Article
Physica D: Nonlinear Phenomena, ISSN 0167-2789, 06/2014, Volume 278-279, pp. 44 - 57
We develop a variational principle that extends the notion of a shearless transport barrier from steady to general unsteady two-dimensional flows and maps... 
Shearless transport barriers | Mixing | Lagrangian coherent structures | Invariant tori | Dynamical systems | MATHEMATICS, APPLIED | PHYSICS, MULTIDISCIPLINARY | PHYSICS, FLUIDS & PLASMAS | CHAOTIC TRANSPORT | PHYSICS, MATHEMATICAL | NONTWIST | TRANSITION | TORI | Algorithms | Tensors | Maps | Two-dimensional flow | Mathematical analysis | Barriers | Unsteady | Transport
Journal Article
Physics of Plasmas, ISSN 1070-664X, 07/2016, Volume 23, Issue 7, p. 72506
We present a numerical study of charged particle motion in a time-independent magnetic field in cylindrical geometry. The magnetic field model consists of an... 
TRANSITION | CHAOS | SEPARATRIX | TRANSPORT | PHYSICS, FLUIDS & PLASMAS | GUIDING-CENTER MOTION | ADIABATIC-INVARIANT | SYSTEMS | PRESERVING NONTWIST MAPS | PHYSICS | Chaotic Dynamics | Nonlinear Sciences | internal transport barrier | PHYSICS OF ELEMENTARY PARTICLES AND FIELDS | magnetic fields | chaos | particle orbits | particle trajectory
Journal Article
Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, ISSN 1539-3755, 05/2009, Volume 79, Issue 5, p. 056215
Cross-jet transport of passive scalars in a kinematic model of the meandering laminar two-dimensional incompressible flow which is known to produce chaotic... 
chaos | PHYSICS, FLUIDS & PLASMAS | SHEAR-FLOW | RECONNECTION | laminar flow | PRESERVING NONTWIST MAPS | jets | MODEL | PHYSICS, MATHEMATICAL | transport processes | CHAOTIC ADVECTION | TRANSITION | bifurcation | FLUID EXCHANGE | DYNAMICS | SYSTEMS | ROSSBY WAVES
Journal Article
Physica D: Nonlinear Phenomena, ISSN 0167-2789, 01/2013, Volume 243, Issue 1, pp. 45 - 63
Journal Article
Chaos: An Interdisciplinary Journal of Nonlinear Science, ISSN 1054-1500, 03/2010, Volume 20, Issue 1, pp. 017514 - 017514-13
The term “Lagrangian coherent structure” (LCS) is normally used to describe numerically detected structures whose properties are similar to those of stable and... 
ZONAL JETS | flow simulation | MATHEMATICS, APPLIED | chaos | MIDDLE ATMOSPHERE | STABILITY | jets | PHYSICS, MATHEMATICAL | TRANSPORT | 2-DIMENSIONAL TURBULENCE | geophysical fluid dynamics | DYNAMICS | SYSTEMS | FLORIDA | atmospheric movements | stratosphere | NONTWIST MAPS | confined flow | Models, Theoretical | Motion | Algorithms | Time Factors | Geology - methods | Models, Statistical | Physics - methods
Journal Article
Communications in Nonlinear Science and Numerical Simulation, ISSN 1007-5704, 2012, Volume 17, Issue 5, pp. 2021 - 2030
► Magnetic field line mappings in tokamaks. ► Nontwist symplectic maps. ► Internal transport barriers in tokamaks. We review symplectic nontwist maps that we... 
Symplectic maps | Nontwist systems | Tokamaks | MATHEMATICS, APPLIED | MAGNETIC-FIELD LINES | PHYSICS, FLUIDS & PLASMAS | BARRIER | PLASMAS | PHYSICS, MATHEMATICAL | TRANSPORT | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | OPERATION | Magnetic fields
Journal Article
Communications in Nonlinear Science and Numerical Simulation, ISSN 1007-5704, 04/2014, Volume 19, Issue 4, pp. 1004 - 1026
Journal Article
Physics Letters A, ISSN 0375-9601, 03/2013, Volume 377, Issue 8, pp. 622 - 627
The breakup of shearless invariant tori with winding number ω=(5−1)/2 (inverse golden mean) is studied using Greeneʼs residue criterion in the recently derived... 
Area-preserving nontwist maps | Greeneʼs residue criterion | Renormalization in dynamical systems | Hamiltonian chaos | Greene's residue criterion | PHYSICS, MULTIDISCIPLINARY | INVARIANT CIRCLES | TRANSITION | CHAOS | TRANSPORT | SYMMETRY | OPERATOR | AREA-PRESERVING MAPS | RENORMALIZATION
Journal Article
European Physical Journal: Special Topics, ISSN 1951-6355, 2008, Volume 165, Issue 1, pp. 195 - 210
The magnetic field line structure in a tokamak can be obtained by direct numerical integration of the field line equations. However, this is a lengthy... 
STANDARD NONTWIST MAP | TWIST MAPS | PHYSICS, MULTIDISCIPLINARY | TOROIDAL GEOMETRY | HAMILTONIAN-SYSTEMS | DYNAMICS | INTERNAL TRANSPORT BARRIERS | REVERSED SHEAR | DIFFUSION | MANIFOLD RECONNECTION | NULL DIVERTOR TOKAMAKS
Journal Article
Nuclear Fusion, ISSN 0029-5515, 05/2012, Volume 52, Issue 5, pp. 54006 - 6
Using Hamiltonian models for the magnetic field lines, we propose a methodology to improve their confinement through the creation of transport barriers. A... 
NONTWIST MAP | CHAOS | PHYSICS, FLUIDS & PLASMAS | ELECTRON-TRANSPORT | Nuclear safety | Confinement | Shear | Nuclear engineering | Tokamak devices | Plasmas | Magnetic fields | Optimization | Plasma Physics | Physics
Journal Article
Physics of Plasmas, ISSN 1070-664X, 09/2008, Volume 15, Issue 9, p. 92310
The existence of a reversed magnetic shear in tokamaks improves the plasma confinement through the formation of internal transport barriers that reduce radial... 
POLOIDAL DIVERTOR | TRANSPORT | PLASMA | STOCHASTIC BOUNDARIES | PHYSICS, FLUIDS & PLASMAS | HOMOCLINIC TANGLES | TORE-SUPRA | HAMILTONIAN-DYNAMICS | PRESERVING NONTWIST MAPS | ENHANCED CONFINEMENT | TEXTOR | MAGNETIC FIELDS | TOKAMAK DEVICES | 70 PLASMA PHYSICS AND FUSION TECHNOLOGY | MAGNETIC SURFACES | REVERSED SHEAR | LIMITERS | WALL EFFECTS | CHAOS THEORY | PLASMA CONFINEMENT
Journal Article
Communications in Nonlinear Science and Numerical Simulation, ISSN 1007-5704, 2012, Volume 17, Issue 5, pp. 2031 - 2044
Journal Article
Communications in Nonlinear Science and Numerical Simulation, ISSN 1007-5704, 2012, Volume 17, Issue 5, pp. 2215 - 2222
► We study the breakup of invariant tori in cubic and quartic nontwist maps. ► Noble and non-noble invariant tori are studied using Greene’s residue criterion.... 
Area-preserving nontwist maps | Greene’s residue criterion | Renormalization in dynamical systems | Hamiltonian chaos | Greene's residue criterion | MATHEMATICS, APPLIED | PHYSICS, FLUIDS & PLASMAS | PHYSICS, MATHEMATICAL | TRANSITION | CHAOS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | SYMMETRY | AREA-PRESERVING MAPS | CHAINS | RENORMALIZATION
Journal Article