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Nonlinear Dynamics

, Volume 78, Issue 3, pp 1629–1643 | Cite as

A pseudo-stable structure in a completely invertible bouncer system

  • Mantas Landauskas
  • Minvydas Ragulskis
Original Paper

Abstract

It is shown that a pseudo-stable structure of non-asymptotic convergence may exist in a completely invertible bouncing ball model. Visualization of the pattern of H-ranks helps to identify this structure. It appears that this structure is similar to the stable manifold of non-invertible nonlinear maps which govern the non-asymptotic convergence to unstable periodic orbits. But this convergence to the unstable repeller of the bouncing ball problem is only temporary since non-asymptotic convergence cannot exist in completely invertible maps. This nonlinear effect is exploited for temporary stabilization of unstable periodic orbits in completely reversible nonlinear maps.

Keywords

Bouncing ball model Rank Manifold Convergence 

Notes

Acknowledgments

Financial support from the Lithuanian Science Council under project No. MIP-100/2012 is acknowledged.

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Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.Research Group for Mathematical and Numerical Analysis of Dynamical SystemsKaunas University of Technology KaunasLithuania
  2. 2.Research Group for Mathematical and Numerical Analysis of Dynamical SystemsKaunas University of Technology KaunasLithuania

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