Advanced Search
Article Contents
Article Contents

Lyapunov exponents and Oseledets decomposition in random dynamical systems generated by systems of delay differential equations



Dedicated to Professor Tomás Caraballo on occasion of his Sixtieth Birthday

The first author is supported by the NCN grant Maestro 2013/08/A/ST1/00275 and the last two authors are partly supported by MICIIN/FEDER under project RTI2018-096523-B-100 and EU Marie-Skłodowska-Curie ITN Critical Transitions in Complex Systems (H2020-MSCA-ITN-2014 643073 CRITICS)

Abstract Full Text(HTML) Related Papers Cited by
  • Linear skew-product semidynamical systems generated by random systems of delay differential equations are considered, both on a space of continuous functions as well as on a space of $ p $-summable functions. The main result states that in both cases, the Lyapunov exponents are identical, and that the Oseledets decompositions are related by natural embeddings.

    Mathematics Subject Classification: Primary: 37H15, 37L55, 34K06.Secondary: 37A30, 60H25.


    \begin{equation} \\ \end{equation}
  • 加载中
  • [1] C. D. Aliprantis and K. C. Border, Infinite Dimensional Analysis. A Hitchhiker's Guide, third edition, Springer, Berlin, 2006. doi: 10.1007/3-540-29587-9.
    [2] L. Arnold, Random Dynamical Systems, Springer Monogr. Math., Springer, Berlin, 1998. doi: 10.1007/978-3-662-12878-7.
    [3] J. A. CalzadaR. Obaya and A. M. Sanz, Continuous separation for monotone skew-product semiflows: From theoretical to numerical results, Discrete Contin. Dyn. Syst. Ser. B, 20 (2015), 915-944.  doi: 10.3934/dcdsb.2015.20.915.
    [4] E. A. Coddington and N. Levinson, Theory of Ordinary Differential Equations, McGraw-Hill, New York, 1955.
    [5] M. C. Delfour and S. K. Mitter, Hereditary differential systems with constant delays. Ⅱ. A class of affine systems and the adjoint problem, J. Differential Equations, 18 (1975), 18-28.  doi: 10.1016/0022-0396(75)90078-9.
    [6] J. Diestel and J. J. Uhl, Jr., Vector Measures, with a foreword by B. J. Pettis, Mathematical Surveys, No. 15, American Mathematical Society, Providence, R.I., 1977. doi: 10.1090/surv/015.
    [7] T. S. Doan, Lyapunov Exponents for Random Dynamical Systems, Ph.D. dissertation, Technische Universität Dresden, 2009.
    [8] G. Froyland, S. Lloyd and A. Quas, A semi-invertible Oseledets theorem with applications to transfer operator cocycles, Discrete Contin. Dyn. Syst., 33 (2013), 3835–3860. doi: 10.3934/dcds.2013.33.3835.
    [9] C. González-Tokman and A. Quas, A semi-invertible operator Oseledets theorem, Ergodic Theory Dynam. Systems, 34 (2014), 1230-1272.  doi: 10.1017/etds.2012.189.
    [10] C. González-Tokman and A. Quas, A concise proof of the multiplicative ergodic theorem on Banach spaces, J. Modern Dynam., 9 (2015), 237-255.  doi: 10.3934/jmd.2015.9.237.
    [11] E. Hille and R. S. Phillips, Functional Analysis and Semi-groups, American Mathematical Society Colloquium Publications, vol. 31. American Mathematical Society, Providence, R. I., 1957.
    [12] Z. Lian and K. Lu, Lyapunov exponents and invariant manifolds for random dynamical systems on a Banach space, Mem. Amer. Math. Soc., 206 (2010). doi: 10.1090/S0065-9266-10-00574-0.
    [13] J. Mierczyński and W. Shen, Principal Lyapunov exponents and principal Floquet spaces of positive random dynamical systems. Ⅰ. General theory, Trans. Amer. Math. Soc., 365 (2013), 5329-5365.  doi: 10.1090/S0002-9947-2013-05814-X.
    [14] J. Mierczyński and W. Shen, Principal Lyapunov exponents and principal Floquet spaces of positive random dynamical systems. Ⅲ. Parabolic equations and delay systems, J. Dynam. Differential Equations, 28 (2016), 1039-1079.  doi: 10.1007/s10884-015-9436-z.
    [15] J. MierczyńskiS. Novo and R. Obaya, Principal Floquet subspaces and exponential separations of type Ⅱ with applications to random delay differential equations, Discrete Contin. Dyn. Syst., 38 (2018), 6163-6193.  doi: 10.3934/dcds.2018265.
  • 加载中

Article Metrics

HTML views(1141) PDF downloads(322) Cited by(0)

Access History

Other Articles By Authors



    DownLoad:  Full-Size Img  PowerPoint