# Harper equation, the dissipative standard map and strange nonchaotic attractors: relationship between an eigenvalue problem and iterated maps

@article{Ketoja1997HarperET, title={Harper equation, the dissipative standard map and strange nonchaotic attractors: relationship between an eigenvalue problem and iterated maps}, author={Jukka A. Ketoja and Indubala I. Satija}, journal={Physica D: Nonlinear Phenomena}, year={1997}, volume={109}, pages={70-80} }

## 46 Citations

Strange Nonchaotic Attractors From a Family of Quasiperiodically Forced Piecewise Linear Maps

- MathematicsInt. J. Bifurc. Chaos
- 2021

It is proved that there exists a unique strange nonchaotic attractor for some set of parameter values which is the graph of an upper semi-continuous function, which is invariant, discontinuous almost everywhere and attracts almost all orbits.

Universal mechanism for the intermittent route to strange nonchaotic attractors in quasiperiodically forced systems

- Physics
- 2004

To examine the universality for the intermittent route to strange nonchaotic attractors (SNAs), we investigate the quasiperiodically forced Henon map, ring map and Toda oscillator which are…

Strange Nonchaotic attractors

- PhysicsInt. J. Bifurc. Chaos
- 2001

The variation of the Lyapunov exponent, and the qualitative and quantitative aspects of its local fluctuation properties, have emerged as an important means of studying fractal attractors, and this analysis finds useful application here.

Thermodynamics of critical strange nonchaotic attractors.

- PhysicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2003

The Tsallis nonextensive entropy which is known to characterize the thermodynamics of systems with leading Lyapunov exponent zero is found to be subadditive for the critical states.

Intermittency route to strange nonchaotic attractors in a non-skew-product map.

- MathematicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2010

This paper derives Badard's non-skew-product map from a periodically driven continuous dynamical system with spatially quasiperiodic potential and investigates onset mechanisms of SNAs in the map, focusing on a transition route to intermittent SNAs.

Reliable Computation of Robust Response Tori on the Verge of Breakdown

- MathematicsSIAM J. Appl. Dyn. Syst.
- 2012

These proofs are based on a reliable computation of the invariant tori and a careful study of their dynamical properties, leading to the rigorous validation of the numerical results with the novel computational techniques.

Critical Strange Nonchaotic Dynamics in the Fibonacci Map

- Physics, MathematicsInt. J. Bifurc. Chaos
- 2005

A driven quasiperiodic skew-product dynamical mapping in which orbits with all Lyapunov exponents equal to zero lie on fractal attractors form a special category of strange nonchaotic attractors (SNAs), and the scenario for their formation is described.

Strange nonchaotic attractors in Harper maps.

- MathematicsChaos
- 2006

It is proved that for a set of parameters of positive measure, the map possesses a SNA, but the set is nowhere dense, because by changing the parameter arbitrarily small amounts, the attractor is a smooth curve and not a S NA.

Quasiperiodically forced interval maps with negative Schwarzian derivative

- Mathematics
- 2003

In the study of quasiperiodically forced systems invariant graphs have a special significance. In some cases, it was already possible to deduce statements about the invariant graphs of certain…

Bubbling route to strange nonchaotic attractor in a nonlinear series LCR circuit with a nonsinusoidal force.

- PhysicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2008

It is found that bubbles appear in the strands of the quasiperiodic attractor due to the instability induced by the additional square-wave-type force, and bubbles then enlarge and get increasingly wrinkled as a function of the control parameter.

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