메뉴 건너뛰기




Volumn 9, Issue 3-4, 2008, Pages 463-492

Nonautonomous finite-time dynamics

Author keywords

Dynamic partition; Hyperbolicity; Nonautonomous differential equations on finite time intervals

Indexed keywords


EID: 45149123185     PISSN: 15313492     EISSN: None     Source Type: Journal    
DOI: 10.3934/dcdsb.2008.9.463     Document Type: Article
Times cited : (22)

References (23)
  • 3
    • 0026792094 scopus 로고
    • The kinematics of stretching and alignment of material elements in general flow fields
    • E. Dresselhaus and M. Tabor, The kinematics of stretching and alignment of material elements in general flow fields, J. Fluid Mech., 236 (1992), 415-444.
    • (1992) J. Fluid Mech. , vol.236 , pp. 415-444
    • Dresselhaus, E.1    Tabor, M.2
  • 4
    • 73149086955 scopus 로고    scopus 로고
    • Hyperbolicity and invariant manifolds for planar nonautonomous systems on finite time intervals, to appear in Internat
    • L. H. Duc and S. Siegmund, Hyperbolicity and invariant manifolds for planar nonautonomous systems on finite time intervals, to appear in Internat. J. Bifur. Chaos Appl. Sci. Engrg.
    • J. Bifur. Chaos Appl. Sci. Engrg.
    • Duc, L.H.1    Siegmund, S.2
  • 5
    • 73149106503 scopus 로고    scopus 로고
    • A bifurcation model for symmetric two-dimensional vortex merger
    • L. H. Due and S. Siegmund, A bifurcation model for symmetric two-dimensional vortex merger, in preparation.
    • Preparation
    • Due, L.H.1    Siegmund, S.2
  • 6
    • 0034147430 scopus 로고    scopus 로고
    • Finding finite-time invariant manifolds in two-dimensional velocity fields
    • (New York, 1998), Chaos
    • G. Haller, Finding finite-time invariant manifolds in two-dimensional velocity fields, Chaotic kinetics and transport (New York, 1998), Chaos, 10 (2000), 99-108.
    • (2000) Chaotic Kinetics and Transport , vol.10 , pp. 99-108
    • Haller, G.1
  • 7
    • 0035505014 scopus 로고    scopus 로고
    • Lagrangian structures and the rate of strain in a partition of two-dimensional turbulence
    • G. Haller, Lagrangian structures and the rate of strain in a partition of two-dimensional turbulence, Phys. Fluids, 13 (2001), 3365-3385.
    • (2001) Phys. Fluids , vol.13 , pp. 3365-3385
    • Haller, G.1
  • 8
    • 0034823558 scopus 로고    scopus 로고
    • Distinguished material surfaces and coherent structures in 3D fluid flows
    • G. Haller, Distinguished material surfaces and coherent structures in 3D fluid flows, Physica D, 149 (2001), 248-277.
    • (2001) Physica D , vol.149 , pp. 248-277
    • Haller, G.1
  • 9
    • 0036612283 scopus 로고    scopus 로고
    • Lagrangian coherent structures from approximate velocity data
    • G. Haller, Lagrangian coherent structures from approximate velocity data, Phys. Fluids A, 14 (2002), 1851-1861.
    • (2002) Phys. Fluids A , vol.14 , pp. 1851-1861
    • Haller, G.1
  • 10
    • 14844284559 scopus 로고    scopus 로고
    • An objective definition of a vortex
    • G. Haller, An objective definition of a vortex, J. Fluid Mech., 525 (2005), 1-26.
    • (2005) J. Fluid Mech. , vol.525 , pp. 1-26
    • Haller, G.1
  • 11
    • 0001229490 scopus 로고    scopus 로고
    • Finite-time transport in aperiodic flows
    • G. Haller and A. C. Poje, Finite-time transport in aperiodic flows, Physica D, 119 (1998),352-380.
    • (1998) Physica D , vol.119 , pp. 352-380
    • Haller, G.1    Poje, A.C.2
  • 12
    • 0034547788 scopus 로고    scopus 로고
    • Lagrangian coherent structures and mixing in two-dimensional turbulence
    • G. Haller and G. Yuan, Lagrangian coherent structures and mixing in two-dimensional turbulence, Physica D, 147 (2000), 352-370.
    • (2000) Physica D , vol.147 , pp. 352-370
    • Haller, G.1    Yuan, G.2
  • 13
    • 0036315576 scopus 로고    scopus 로고
    • Distinguished hyperbolic trajectories in time-dependent fluid flows: Analytical and computational approach for velocity fields defined as data sets
    • K. Ide, D. Small and S. Wiggins, Distinguished hyperbolic trajectories in time-dependent fluid flows: analytical and computational approach for velocity fields defined as data sets, Nonlinear Processes in Geophysics, 9 (2002), 237-263.
    • (2002) Nonlinear Processes in Geophysics , vol.9 , pp. 237-263
    • Ide, K.1    Small, D.2    Wiggins, S.3
  • 14
    • 0041377838 scopus 로고    scopus 로고
    • Existence and computation of hyperbolic trajectories of aperiodically time dependent vector fields and their approximations
    • N. Ju, D. Small and S. Wiggins, Existence and computation of hyperbolic trajectories of aperiodically time dependent vector fields and their approximations, Internat. J. Bifur. Chaos Appl. Sci. Engrg., 13 (2002), 1449-1457.
    • (2002) Internat. J. Bifur. Chaos Appl. Sci. Engrg. , vol.13 , pp. 1449-1457
    • Ju, N.1    Small, D.2    Wiggins, S.3
  • 15
    • 0008112282 scopus 로고
    • Perturbation Theory for Linear Operators
    • Reprint of the 1980 edition, Springer-Verlag, Berlin
    • T. Kato, "Perturbation Theory for Linear Operators," Reprint of the 1980 edition. Classics in Mathematics, Springer-Verlag, Berlin, 1995.
    • (1995) Classics in Mathematics
    • Kato, T.1
  • 16
    • 34250616203 scopus 로고    scopus 로고
    • Lagrangian coherent structures in N-dimensional systems
    • published electronically
    • F. Lekien, S. C. Shadden and J. E. Marsden, Lagrangian coherent structures in N-dimensional systems, J. Math. Phys., 48 (2007), published electronically.
    • (2007) J. Math. Phys. , vol.48
    • Lekien, F.1    Shadden, S.C.2    Marsden, J.E.3
  • 17
    • 0001549406 scopus 로고    scopus 로고
    • Geometric structures, lobe dynamics, and Lagrangian transport in flows with aperiodic time-dependence, with applications to Rossby wave flow
    • N. Malhotra and S. Wiggins, Geometric structures, lobe dynamics, and Lagrangian transport in flows with aperiodic time-dependence, with applications to Rossby wave flow, J. Nonlinear Sci., 8 (1998), 401-456.
    • (1998) J. Nonlinear Sci. , vol.8 , pp. 401-456
    • Malhotra, N.1    Wiggins, S.2
  • 18
    • 0041529987 scopus 로고    scopus 로고
    • Computation of stable and unstable manifolds of hyperbolic trajectories in two-dimensional, aperiodically time-dependent vector fields
    • A. Mancho, D. Small, S. Wiggins and K. Ide, Computation of stable and unstable manifolds of hyperbolic trajectories in two-dimensional, aperiodically time-dependent vector fields, Phys. D, 182 (2003), 188-222.
    • (2003) Phys. D , Issue.182 , pp. 188-222
    • Mancho, A.1    Small, D.2    Wiggins, S.3    Ide, K.4
  • 19
    • 1842682569 scopus 로고    scopus 로고
    • Computation of hyperbolic trajectories and their stable and unstable manifolds for oceanographie flows represented as data sets
    • A. Mancho, D. Small and S. Wiggins, Computation of hyperbolic trajectories and their stable and unstable manifolds for oceanographie flows represented as data sets, Nonlinear Processes in Geophysics, 11 (2004), 17-33.
    • (2004) Nonlinear Processes in Geophysics , vol.11 , pp. 17-33
    • Mancho, A.1    Small, D.2    Wiggins, S.3
  • 20
    • 22244477095 scopus 로고    scopus 로고
    • Quantifying transport in numerically generated velocity fields
    • P. D. Miller, C. K. R. T. Jones, A. M. Rogerson and L. J. Pratt, Quantifying transport in numerically generated velocity fields, Phys. D, 110 (1997), 105-122.
    • (1997) Phys. D , vol.110 , pp. 105-122
    • Miller, P.D.1    Jones, C.K.R.T.2    Rogerson, A.M.3    Pratt, L.J.4
  • 22
    • 28244461621 scopus 로고    scopus 로고
    • Definition and properties of Lagrangian coherent structures from finite-time Lyapunov exponents in two-dimensional aperiodic flows
    • S. C. Shadden, P. Lekien and J. E. Marsden, Definition and properties of Lagrangian coherent structures from finite-time Lyapunov exponents in two-dimensional aperiodic flows, Physica D, 212 (2005), 271-304.
    • (2005) Physica D , vol.212 , pp. 271-304
    • Shadden, S.C.1    Lekien, P.2    Marsden, J.E.3
  • 23
    • 0035322316 scopus 로고    scopus 로고
    • Chaotic advection by two interacting finite-area vortices
    • O. U. Velasco Puentes, Chaotic advection by two interacting finite-area vortices, Phys. Fluids, 13 (2001), 901-912.
    • (2001) Phys. Fluids , vol.13 , pp. 901-912
    • Velasco Puentes, O.U.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.