Advanced Search
Article Contents
Article Contents

Dynamical systems with a prescribed globally bp-attracting set and applications to conservative dynamics

Abstract Full Text(HTML) Related Papers Cited by
  • Given an arbitrary fixed closed subset $ \mathcal{C}\subset\mathbb{R}^n $, we provide an explicit method to construct a dynamical system which admits the regular part of $ \mathcal{C} $ as globally bp-attracting set, i.e. a closed and invariant set which attracts every bounded positive orbit of the dynamical system. As application, we provide an explicit method of leafwise asymptotic bp-stabilization of the regular part of an a-priori given invariant set of a conservative system. The theoretical results are illustrated for the completely integrable case of the Rössler dynamical system.

    Mathematics Subject Classification: Primary: 34C45; Secondary: 37J15; 70H33.


    \begin{equation} \\ \end{equation}
  • 加载中
  • [1] G.-I. BischiC. Mira and L. Gardini, Unbounded sets of attraction, Internat. J. Bifur. Chaos Appl. Sci. Engrg., 10 (2000), 1437-1469.  doi: 10.1142/S0218127400000980.
    [2] A. N. Carvalho, J. A. Langa and J. C. Robinson, Attractors for Infinite-Dimensional Non-Autonomous Dynamical Systems, Applied Mathematical Sciences, 182. Springer, New York, 2013. doi: 10.1007/978-1-4614-4581-4.
    [3] B. Günther and J. Segal, Every attractor of a flow on a manifold has the shape of a finite polyhedron, Proc. Amer. Math. Soc., 119 (1993), 321-329.  doi: 10.1090/S0002-9939-1993-1170545-4.
    [4] B. Günther, Construction of differentiable flows with prescribed attractor, Topology Appl., 62 (1995), 87-91.  doi: 10.1016/0166-8641(94)00047-7.
    [5] J. K. Hale, Asymptotic Behavior of Dissipative Systems, Mathematical Surveys and Monographs, 25. American Mathematical Society, Providence, 1988.
    [6] P. Hartman, Ordinary Differential Equations, Classics in Applied Mathematics, 38. SIAM, Philadelphia, PA, 2002. doi: 10.1137/1.9780898719222.
    [7] J. M. Lee, Introduction to Smooth Manifolds, Second edition, Graduate Texts in Mathematics, 218. Springer, New York, 2013.
    [8] T. S. RatiuR. M. TudoranL. SbanoE. Sousa Dias and G. Terra, Chapter II: A crash course in geometric mechanics, London Math. Soc. Lecture Note Ser., Geometric mechanics and symmetry, Cambridge Univ. Press, Cambridge, 306 (2005), 23-156.  doi: 10.1017/CBO9780511526367.003.
    [9] J. C. RobinsonDimensions, Embeddings, and Attractors, Cambridge Tracts in Mathematics, 186. Cambridge University Press, Cambridge, 2011. 
    [10] R. M. Tudoran and A. G\^irban, On the completely integrable case of the Rössler system, J. Math. Phys., 53 (2012), 052701, 10 pp. doi: 10.1063/1.4708621.
    [11] R. M. Tudoran, Affine distributions on Riemannian manifolds with applications to dissipative dynamics, J. Geom. Phys., 92 (2015), 55-68.  doi: 10.1016/j.geomphys.2015.01.017.
    [12] R. M. Tudoran, Asymptotic bp-stabilization of a given closed invariant set of a smooth dynamical system, J. Differential Equations, 267 (2019), 3768-3777.  doi: 10.1016/j.jde.2019.04.013.
  • 加载中

Article Metrics

HTML views(274) PDF downloads(197) Cited by(0)

Access History

Other Articles By Authors



    DownLoad:  Full-Size Img  PowerPoint