Isaac Scientific Publishing

Journal of Advances in Applied Mathematics

Invariant Unstable Manifolds of Nonautonomous Systems on Time Scales

Download PDF (264.9 KB) PP. 37 - 44 Pub. Date: April 1, 2019

DOI: 10.22606/jaam.2019.42001


  • Le Huy Tien1, Nguyen Minh Man2
    1Department of Mathematics, Mechanics and Informatics, Vietnam National University at Hanoi, 334 Nguyen Trai, Thanh Xuan, Hanoi, Viet Nam
  • Le Duc Nhien1*
    2Faculty of Basic Sciences, Ha Noi University of Mining and Geology, 18 Pho Vien, Ha Noi, Viet Nam


This paper is concerned with the existence of invariant manifolds for dynamical equations on a periodic time scale when the nonlinear perturbation has a small global Lipschitz constant. Particularly, for time-varying non-regressive dynamical equations, which have exponential dichotomies on a periodic time scale with bounded graininess, we use the method of graph transforms as in [1] to prove that there exists a unique integral manifold of that systems.


Integral manifold, graph transforms, time scales, linear dynamic equation.


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