메뉴 건너뛰기




Volumn 136, Issue 647, 1998, Pages

Almost automorphic and almost periodic dynamics in skew-product semiflows

Author keywords

Almost automorphy; Almost periodicity; Fourier analysis; Harmonics and subharmonics; Lifting property; Monotone dynamics; Skew product semiflow; Stability; Topological dynamics

Indexed keywords


EID: 0013080113     PISSN: 00659266     EISSN: None     Source Type: Journal    
DOI: 10.1090/memo/0647     Document Type: Article
Times cited : (294)

References (61)
  • 1
    • 84942222028 scopus 로고
    • The Zero Set of a Solution of a Parabolic Equation
    • S. B. Angenent, The Zero Set of a Solution of a Parabolic Equation, J. Reine Angew. Math. 390 (1988).
    • (1988) J. Reine Angew. Math. , vol.390
    • Angenent, S.B.1
  • 2
    • 0001583347 scopus 로고
    • Convergence in General Periodic Parabolic Equations in One Space Dimension
    • TMA
    • P. Brunovský, P. Poláčik and B. Sandstede, Convergence in General Periodic Parabolic Equations in One Space Dimension, Nonl. Anal., TMA 18 (1992).
    • (1992) Nonl. Anal. , vol.18
    • Brunovský, P.1    Poláčik, P.2    Sandstede, B.3
  • 3
    • 0001640367 scopus 로고
    • The Discrete Lyapunov Function for Scalar Differential Delay Equations
    • Y. Cao, The Discrete Lyapunov Function for Scalar Differential Delay Equations, J. Diff. Eqs. 87 (1990).
    • (1990) J. Diff. Eqs. , vol.87
    • Cao, Y.1
  • 4
    • 0001731871 scopus 로고
    • Instability Results for Reaction-diffusion Equations with Neumann Boundary Conditions
    • R. C. Casten and C. J. Holland, Instability Results for Reaction-diffusion Equations with Neumann Boundary Conditions, J. Diff. Eqs. 27 (1978).
    • (1978) J. Diff. Eqs. , vol.27
    • Casten, R.C.1    Holland, C.J.2
  • 5
    • 0010195359 scopus 로고
    • Asymptotic Behavior for Solutions of a One-Dimensional Parabolic Equation with Homogeneous Neumann Boundary Conditions
    • N. Chafee, Asymptotic Behavior for Solutions of a One-Dimensional Parabolic Equation with Homogeneous Neumann Boundary Conditions, J. Diff. Eqs. 18 (1975).
    • (1975) J. Diff. Eqs. , vol.18
    • Chafee, N.1
  • 6
    • 0000645209 scopus 로고
    • Structural Stability for Time-periodic One-dimensional Parabolic Equations
    • M. Chen, X. Y. Chen and J. K. Hale, Structural Stability for Time-periodic One-dimensional Parabolic Equations, J. Diff. Eqs. 96 (1992).
    • (1992) J. Diff. Eqs. , vol.96
    • Chen, M.1    Chen, X.Y.2    Hale, J.K.3
  • 8
    • 50849145650 scopus 로고
    • Convergence, Asymptotic Periodicity, and Finite-Point Blow-Up in One-Dimensional Semilinear Heat Equations
    • X.-Y. Chen and H. Matano, Convergence, Asymptotic Periodicity, and Finite-Point Blow-Up in One-Dimensional Semilinear Heat Equations, J. Diff. Eqs. 78 (1989).
    • (1989) J. Diff. Eqs. , vol.78
    • Chen, X.-Y.1    Matano, H.2
  • 9
    • 0003287946 scopus 로고
    • Gradient-like Structure and Morse Decompositions for Time-periodic One-dimensional Parabolic Equations
    • X.-Y. Chen and P. Poláčik, Gradient-like Structure and Morse Decompositions for Time-periodic One-dimensional Parabolic Equations, J. Dyn. and Diff. Eqs. 7 (1995).
    • (1995) J. Dyn. and Diff. Eqs. , vol.7
    • Chen, X.-Y.1    Poláčik, P.2
  • 11
    • 0000720910 scopus 로고
    • Center Manifold and Stability for Skew-product Flows
    • S.-N. Chow and Y. Yi, Center Manifold and Stability for Skew-product Flows, J. Dyn. and Diff. Eqs. 6 (1994).
    • (1994) J. Dyn. and Diff. Eqs. , vol.6
    • Chow, S.-N.1    Yi, Y.2
  • 12
    • 0001147857 scopus 로고
    • Stable Subharmonic Solutions in Periodic Reaction-Diffusion Equations
    • E. N. Dancer and P. Hess, Stable Subharmonic Solutions in Periodic Reaction-Diffusion Equations, J. Diff. Eqs. 108 (1994).
    • (1994) J. Diff. Eqs. , vol.108
    • Dancer, E.N.1    Hess, P.2
  • 13
    • 51249194812 scopus 로고
    • Sur les Équations Différentielles Linéaires á Coefficients Presque-Périodiques
    • J. Favard, Sur les Équations Différentielles Linéaires á Coefficients Presque-Périodiques, Acta Math. (2) 51 (1927).
    • (1927) Acta Math. , vol.51 , Issue.2
    • Favard, J.1
  • 20
    • 0003744101 scopus 로고
    • Asymptotic Behavior of Dissipative Systems
    • Amer. Math. Soc., Providence, RI
    • _, Asymptotic Behavior of Dissipative Systems, Mathematical Surveys and Monographs, Amer. Math. Soc., Providence, RI, 1988.
    • (1988) Mathematical Surveys and Monographs
  • 21
    • 0003304963 scopus 로고
    • Geometric Theory of Semilinear Parabolic Equations
    • Springer-Verlag, Berlin
    • D. Henry, Geometric Theory of Semilinear Parabolic Equations, Lecture Notes in Math., vol. 840, Springer-Verlag, Berlin, 1981.
    • (1981) Lecture Notes in Math. , vol.840
    • Henry, D.1
  • 22
    • 0000735195 scopus 로고
    • Spatial Homogeneity of Stable Solutions of Some Periodic-parabolic Problems with Neumann Boundary Conditions
    • P. Hess, Spatial Homogeneity of Stable Solutions of Some Periodic-parabolic Problems with Neumann Boundary Conditions, J. Diff. Eqs. 68 (1987).
    • (1987) J. Diff. Eqs. , vol.68
    • Hess, P.1
  • 23
    • 21144459956 scopus 로고
    • Boundedness of Prime Periods of Stable Cycles and Convergence to Fixed Points in Discrete Monotone Dynamical Systems
    • P. Hess and P. Poláčik, Boundedness of Prime Periods of Stable Cycles and Convergence to Fixed Points in Discrete Monotone Dynamical Systems, SIAM J. Math. Anal. 24 (1993).
    • (1993) SIAM J. Math. Anal. , vol.24
    • Hess, P.1    Poláčik, P.2
  • 24
    • 0025067902 scopus 로고
    • Convergence to Spatial-temporal Clines in the Fisher Equation with Time-periodic Fitnesses
    • P. Hess and H. Weinberger, Convergence to Spatial-temporal Clines in the Fisher Equation with Time-periodic Fitnesses, J. Math. Biol. 28 (1990).
    • (1990) J. Math. Biol. , vol.28
    • Hess, P.1    Weinberger, H.2
  • 25
    • 85012593635 scopus 로고
    • On a Floquet Theory for Almost Periodic Two-dimensional Linear Systems
    • R. A. Johnson, On a Floquet Theory for Almost Periodic Two-dimensional Linear Systems, J. Diff. Eqs. 37 (1980).
    • (1980) J. Diff. Eqs. , vol.37
    • Johnson, R.A.1
  • 26
    • 84966204365 scopus 로고
    • A Linear Almost Periodic Equations with an Almost Automorphic Solution
    • _, A Linear Almost Periodic Equations with an Almost Automorphic Solution, Proc. Amer. Math. Soc. 82 (1981).
    • (1981) Proc. Amer. Math. Soc. , vol.82
  • 27
    • 84972496687 scopus 로고
    • Bounded Solutions of Scalar Almost Periodic Linear Equations
    • _, Bounded Solutions of Scalar Almost Periodic Linear Equations, Illinois J. Math. 25 (1981).
    • (1981) Illinois J. Math. , vol.25
  • 28
    • 0010119802 scopus 로고
    • On Almost-Periodic Linear Differential Systems of Millionščikov and Vinograd
    • _, On Almost-Periodic Linear Differential Systems of Millionščikov and Vinograd, J. Math. Anal. Appl. 85 (1982).
    • (1982) J. Math. Anal. Appl. , vol.85
  • 29
    • 84966260264 scopus 로고
    • Linear Differential Systems with Interval Spectrum
    • _, Linear Differential Systems with Interval Spectrum, Proc. Amer. Math. Soc. 80 (1980).
    • (1980) Proc. Amer. Math. Soc. , vol.80
  • 31
    • 0000226142 scopus 로고
    • Morse Decompositions for Delay-Differential Equations
    • J. Mallet-Paret, Morse Decompositions for Delay-Differential Equations, J. Diff. Eqs. 72 (1988).
    • (1988) J. Diff. Eqs. , vol.72
    • Mallet-Paret, J.1
  • 32
    • 51249182088 scopus 로고
    • Almost Automorphic Symbolic Minimal Sets without Unique Ergodicity
    • N. G. Markley and M. E. Paul, Almost Automorphic Symbolic Minimal Sets without Unique Ergodicity, Israel J. of Math. 34 (1979).
    • (1979) Israel J. of Math. , vol.34
    • Markley, N.G.1    Paul, M.E.2
  • 33
    • 0000657925 scopus 로고
    • Nonincrease of the Lap-number of a Solution for a One dimensional Semilinear Parabolic Equation
    • H. Matano, Nonincrease of the Lap-number of a Solution for a One dimensional Semilinear Parabolic Equation, J. Fac. Sci. Univ. Tokyo Sect. IA 29 (1982).
    • (1982) J. Fac. Sci. Univ. Tokyo Sect. IA , vol.29
    • Matano, H.1
  • 34
    • 85009592686 scopus 로고
    • Asymptotic Behavior and Stability of Solutions of Semilinear Diffusion Equations
    • _, Asymptotic Behavior and Stability of Solutions of Semilinear Diffusion Equations, Publ. Res. Inst. Math. Sci. Kyoto Univ. 15 (1979).
    • (1979) Publ. Res. Inst. Math. Sci. Kyoto Univ. , vol.15
  • 35
    • 0000581034 scopus 로고
    • Almost Periodic Differential Equations as Dynamical Systems with Applications to the Existence of a. p. Solutions
    • R. K. Miller, Almost Periodic Differential Equations as Dynamical Systems with Applications to the Existence of a. p. Solutions, J. Diff. Eqs. 1 (1965).
    • (1965) J. Diff. Eqs. , vol.1
    • Miller, R.K.1
  • 36
    • 0000331882 scopus 로고
    • Complicated Dynamics in Scalar Semilinear Parabolic Equations in Higher Space Dimension
    • P. Poláčik, Complicated Dynamics in Scalar Semilinear Parabolic Equations in Higher Space Dimension, J. Diff. Eqs. 89 (1991).
    • (1991) J. Diff. Eqs. , vol.89
    • Poláčik, P.1
  • 37
    • 0002553143 scopus 로고
    • Convergence in Smooth Strongly Monotone Flows Defined by Semilinear Parabolic Equations
    • _, Convergence in Smooth Strongly Monotone Flows Defined by Semilinear Parabolic Equations, J. Diff. Eqs. 79 (1989).
    • (1989) J. Diff. Eqs. , vol.79
  • 38
    • 34249916235 scopus 로고
    • Convergence to Cycles as a Typical Asymptotic Behavior in Smooth Strongly Monotone Discrete-Time Dynamical Systems
    • P. Poláčik and I. Tereščák, Convergence to Cycles as a Typical Asymptotic Behavior in Smooth Strongly Monotone Discrete-Time Dynamical Systems, Arch. Rat. Mech. Anal. 116 (1991).
    • (1991) Arch. Rat. Mech. Anal. , vol.116
    • Poláčik, P.1    Tereščák, I.2
  • 39
    • 0010073453 scopus 로고
    • Exponential Separation and Invariant Bundles for Maps in Ordered Banach Spaces with Applications to Parabolic Equations
    • _, Exponential Separation and Invariant Bundles for Maps in Ordered Banach Spaces with Applications to Parabolic Equations, J. Diff. Eqs. 5 (1993).
    • (1993) J. Diff. Eqs. , vol.5
  • 41
    • 0001230297 scopus 로고
    • Existence of Dichotomics and Invariant Splittings for Linear Differential Equations III
    • R. J. Sacker and G. R. Sell, Existence of Dichotomics and Invariant Splittings for Linear Differential Equations III, J. Diff. Eqs. 22 (1976).
    • (1976) J. Diff. Eqs. , vol.22
    • Sacker, R.J.1    Sell, G.R.2
  • 42
    • 49349126301 scopus 로고
    • A Spectral Theory for Linear Differential Systems
    • _, A Spectral Theory for Linear Differential Systems, J. Diff. Eqs. 27 (1978).
    • (1978) J. Diff. Eqs. , vol.27
  • 43
    • 0003298777 scopus 로고
    • Lifting Properties in Skew-Product Flows with Applications to Differential Equations
    • _, Lifting Properties in Skew-Product Flows with Applications to Differential Equations, Memoirs Amer. Math. Soc. 11 (1977).
    • (1977) Memoirs Amer. Math. Soc. , vol.11
  • 44
    • 67649318175 scopus 로고
    • Nonautonomous Differential Equations and Topological Dynamics I, II
    • G. R. Sell, Nonautonomous Differential Equations and Topological Dynamics I, II, Trans. Amer. Math. Soc. 127 (1967).
    • (1967) Trans. Amer. Math. Soc. , vol.127
    • Sell, G.R.1
  • 46
    • 0000113683 scopus 로고
    • Dynamics of Almost Periodic Scalar Parabolic Equations
    • W. Shen and Y. Yi, Dynamics of Almost Periodic Scalar Parabolic Equations, J. Diff. Eqs. 122 (1995).
    • (1995) J. Diff. Eqs. , vol.122
    • Shen, W.1    Yi, Y.2
  • 47
    • 0000392620 scopus 로고
    • Asymptotic Almost Periodicity of Scalar Parabolic Equations with Almost Periodic Time Dependence
    • _, Asymptotic Almost Periodicity of Scalar Parabolic Equations with Almost Periodic Time Dependence, J. Diff. Eqs. 122 (1995).
    • (1995) J. Diff. Eqs. , vol.122
  • 48
    • 33749269869 scopus 로고
    • On Minimal Sets of Scalar Parabolic Equations with Skew-product Structures
    • _, On Minimal Sets of Scalar Parabolic Equations with Skew-product Structures, Trans. Amer. Math. Soc. 347 (1995).
    • (1995) Trans. Amer. Math. Soc. , vol.347
  • 49
    • 2942654553 scopus 로고    scopus 로고
    • Ergodicity of Minimal Sets in Scalar Parabolic Equations
    • _, Ergodicity of Minimal Sets in Scalar Parabolic Equations, J. Dyn. and Diff. Eqs. 8 (1996).
    • (1996) J. Dyn. and Diff. Eqs. , vol.8
  • 50
    • 0001243427 scopus 로고
    • Monotone Semiflows Generated by Functional Differential Equations
    • H. L. Smith, Monotone Semiflows Generated by Functional Differential Equations, J. Diff. Eqs. 66 (1987).
    • (1987) J. Diff. Eqs. , vol.66
    • Smith, H.L.1
  • 51
    • 0001676484 scopus 로고
    • Strongly Order Preserving Semiflows generated by Functional Differential Equations
    • H. L. Smith and H. R. Thieme, Strongly Order Preserving Semiflows generated by Functional Differential Equations, J. Diff. Eqs. 93 (1991).
    • (1991) J. Diff. Eqs. , vol.93
    • Smith, H.L.1    Thieme, H.R.2
  • 52
    • 0001043836 scopus 로고
    • Linearly Stable Subharmonic Orbits in Strongly Monotone Time-periodic Dynamical Systems
    • P. Takáč, Linearly Stable Subharmonic Orbits in Strongly Monotone Time-periodic Dynamical Systems, Proc. Amer. Math. Soc. 115 (1992).
    • (1992) Proc. Amer. Math. Soc. , vol.115
    • Takáč, P.1
  • 53
    • 0000055435 scopus 로고
    • A Construction of Stable Subharmonic Orbits in Monotone Time-periodic Dynamical Systems
    • _, A Construction of Stable Subharmonic Orbits in Monotone Time-periodic Dynamical Systems, Mh. Math. 115 (1993).
    • (1993) Mh. Math. , vol.115
  • 54
    • 0003345839 scopus 로고
    • On a Theorem of Bochner
    • W. A. Veech, On a Theorem of Bochner, Ann. Math. 86 (1967).
    • (1967) Ann. Math. , vol.86
    • Veech, W.A.1
  • 55
    • 0000996366 scopus 로고
    • Almost Automorphic Functions on Groups
    • _, Almost Automorphic Functions on Groups, Amer. J. Math. 87 (1965).
    • (1965) Amer. J. Math. , vol.87
  • 56
    • 0001335516 scopus 로고
    • A Problem Suggested by N. P. Erugin
    • R. E. Vinograd, A Problem Suggested by N. P. Erugin, Diff. Eqs. 11 (1975).
    • (1975) Diff. Eqs. , vol.11
    • Vinograd, R.E.1
  • 57
    • 0010195362 scopus 로고
    • N, I. Global Stabilization Process
    • N, I. Global Stabilization Process, J. Diff. Eqs. 94 (1991).
    • (1991) J. Diff. Eqs. , vol.94
    • Vuillermot, P.1
  • 58
    • 33749289644 scopus 로고
    • N, II. Codimension-One Stable Manifolds
    • N, II. Codimension-One Stable Manifolds, Diff. Int. Eqs. 5 (1991);
    • (1991) Diff. Int. Eqs. , vol.5
  • 59
    • 33749290768 scopus 로고
    • III. Center Curves and Liapounov Stability
    • III. Center Curves and Liapounov Stability, Nonl. Anal. TMA 22 (1994).
    • (1994) Nonl. Anal. TMA , vol.22
  • 60
    • 0010119081 scopus 로고
    • Bounded and Almost Periodic Solutions of Semi-linear Parabolic Equations
    • J. R. Ward, Jr., Bounded and Almost Periodic Solutions of Semi-linear Parabolic Equations, Rocky Mountain J. Math. 18 (1988).
    • (1988) Rocky Mountain J. Math. , vol.18
    • Ward Jr., J.R.1
  • 61
    • 0010072517 scopus 로고
    • Almost Automorphic Solutions of Certain Abstract Differential Equations
    • M. Zaki, Almost Automorphic Solutions of Certain Abstract Differential Equations, Ann. Mat. Pura Appl. 101 (1974).
    • (1974) Ann. Mat. Pura Appl. , vol.101
    • Zaki, M.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.