Nonlinear Dynamics

, Volume 94, Issue 4, pp 2613–2624 | Cite as

On sample-based computations of invariant sets

  • Shen Zeng
Original Paper


In this paper, the classical problem of uncovering the maximal invariant set of a (discrete-time) dynamical system is illuminated from a novel perspective, which in particular leads to a novel sample-based computational procedure to compute the invariant set. The mathematical description of these new insights can be formulated in strikingly basic set-theoretic terms, and more importantly, be efficiently realized computationally in terms of different sample-based implementations. We illustrate the simplicity and efficiency of the computational method on three examples with a maximal invariant set that is unstable in both time directions, the classical Hénon map, a three-dimensional analogue of the Hénon map, and a Van der Pol oscillator.


Discrete-time dynamical systems Invariant set Sample-based techniques 


Compliance with ethical standards

Conflicts of interest

The author declares that he has no conflict of interest.


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© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.Department of Electrical and Systems EngineeringWashington UniversitySt. LouisUSA

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