## Journals

- Advances in Mathematics of Communications
- Big Data & Information Analytics
- Communications on Pure & Applied Analysis
- Discrete & Continuous Dynamical Systems - A
- Discrete & Continuous Dynamical Systems - B
- Discrete & Continuous Dynamical Systems - S
- Evolution Equations & Control Theory
- Inverse Problems & Imaging
- Journal of Computational Dynamics
- Journal of Dynamics & Games
- Journal of Geometric Mechanics
- Journal of Industrial & Management Optimization
- Journal of Modern Dynamics
- Kinetic & Related Models
- Mathematical Biosciences & Engineering
- Mathematical Control & Related Fields
- Mathematical Foundations of Computing
- Networks & Heterogeneous Media
- Numerical Algebra, Control & Optimization
- Electronic Research Announcements
- Conference Publications
- AIMS Mathematics

ERA-MS

We study the splitting of invariant manifolds of whiskered tori with two or
three frequencies in nearly-integrable Hamiltonian systems,
such that the hyperbolic part is given by a pendulum.
We consider a 2-dimensional torus with
a frequency vector $\omega=(1,\Omega)$, where $\Omega$ is a quadratic
irrational number, or a 3-dimensional torus with a frequency vector
$\omega=(1,\Omega,\Omega^2)$, where $\Omega$ is a cubic irrational number.
Applying the Poincaré--Melnikov method, we find exponentially small
asymptotic estimates for the maximal splitting distance between the stable and
unstable manifolds associated to the invariant torus, and we show that such
estimates depend strongly on the arithmetic properties of the frequencies. In
the quadratic case, we use the continued fractions theory to establish a
certain arithmetic property, fulfilled in 24 cases, which allows us to provide
asymptotic estimates in a simple way. In the cubic case, we focus our attention
to the case in which $\Omega$ is the so-called cubic golden number (the real
root of $x^3+x-1=0$), obtaining also asymptotic estimates. We point out the
similitudes and differences between the results obtained for both the quadratic
and cubic cases.

## Year of publication

## Related Authors

## Related Keywords

[Back to Top]