# Resonances within chaos.

@article{Gallavotti2011ResonancesWC, title={Resonances within chaos.}, author={Giovanni Gallavotti and Guido Gentile and Alessandro Giuliani}, journal={Chaos}, year={2011}, volume={22 2}, pages={ 026108 } }

A chaotic system under periodic forcing can develop a periodically visited strange attractor. We discuss simple models in which the phenomenon, quite easy to see in numerical simulations, can be completely studied analytically.

## 6 Citations

### Construction of the Lyapunov Spectrum in a Chaotic System Displaying Phase Synchronization

- Mathematics
- 2015

We consider a three-dimensional chaotic system consisting of the suspension of Arnold’s cat map coupled with a clock via a weak dissipative interaction. We show that the coupled system displays a…

### Construction of the Lyapunov Spectrum in a Chaotic System Displaying Phase Synchronization

- MathematicsMathematical Physics, Analysis and Geometry
- 2016

We consider a three-dimensional chaotic system consisting of the suspension of Arnold’s cat map coupled with a clock via a weak dissipative interaction. We show that the coupled system displays a…

### Oscillator Synchronisation under Arbitrary Quasi-periodic Forcing

- Mathematics
- 2012

We study the problem of existence of response solutions for a real-analytic one-dimensional system, consisting of a rotator subject to a small quasi-periodic forcing with Bryuno frequency vector. We…

### Introduction to Focus Issue: statistical mechanics and billiard-type dynamical systems.

- PhysicsChaos
- 2012

This Focus Issue presents the recent progress inynamical systems of the billiard type with contributions from the mathematical as well as physical stand point.

### Convergent series for quasi-periodically forced strongly dissipative systems

- Mathematics
- 2012

We study the ordinary differential equation eẍ + ẋ + eg(x) = ef(ωt), with f and g analytic and f quasi-periodic in t with frequency vector ω ∈ ℝd. We show that if there exists c0 ∈ ℝ such that g(c0)…

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