Add to ORKGWe establish an analytically computable formula based on the adiabatic Melnikov function for lobe area in one-degree-of-freedom Hamiltonian systems depending on a parameter which varies slowly in time. We illustrate this lobe area result on a slowly, parametrically forced pendulum, a paradigm problem for adiabatic chaos. Our analysis unites the theory of action from classical mechanics with the theory of the adiabatic Melnikov function from the field of global bifurcation theory
Melnikov’s method is applied to the planar double pendulum proving it to be a chaotic system. The pa...
Cornerstone models of physics, from the semi-classical mechanics in atomic and molecular physics to ...
Adiabatic invariants for dynamical systems with one degree of freedom are derived. The method develo...
We establish an analytically computable formula based on the adiabatic Melnikov function for lobe ar...
Trapping phenomena involving non-linear resonances have been considered in the past in the framework...
Abstract. The Kolmagorov entropy of a model Ar, cluster converges smoothly to its limiting value whe...
We study the dependence of the chaotic layer width in spatially periodic non-autonomous Hamiltonian ...
We study a new problem of adiabatic invariance, namely a nonlinear oscillator with slowly moving cen...
The adiabatic theorem is a fundamental result in quantum mechanics, which states that a system can b...
summary:The two-parameter Hamiltonian system with the autonomous perturbation is considered. Via the...
In many problems of classical mechanics and theoretical physics dynamics can be described as a slow ...
This paper is devoted to the analysis of bifurcations of limit cycles in planar polynomial near-Hami...
We consider one-dimensional classical time-dependent Hamiltonian systems with quasi-periodic orbits....
AbstractWe study the problem of exponentially small splitting of separatrices of one degree of freed...
In this paper, results concerning the phenomenon of adiabatic trapping into resonance for a class of...
Melnikov’s method is applied to the planar double pendulum proving it to be a chaotic system. The pa...
Cornerstone models of physics, from the semi-classical mechanics in atomic and molecular physics to ...
Adiabatic invariants for dynamical systems with one degree of freedom are derived. The method develo...
We establish an analytically computable formula based on the adiabatic Melnikov function for lobe ar...
Trapping phenomena involving non-linear resonances have been considered in the past in the framework...
Abstract. The Kolmagorov entropy of a model Ar, cluster converges smoothly to its limiting value whe...
We study the dependence of the chaotic layer width in spatially periodic non-autonomous Hamiltonian ...
We study a new problem of adiabatic invariance, namely a nonlinear oscillator with slowly moving cen...
The adiabatic theorem is a fundamental result in quantum mechanics, which states that a system can b...
summary:The two-parameter Hamiltonian system with the autonomous perturbation is considered. Via the...
In many problems of classical mechanics and theoretical physics dynamics can be described as a slow ...
This paper is devoted to the analysis of bifurcations of limit cycles in planar polynomial near-Hami...
We consider one-dimensional classical time-dependent Hamiltonian systems with quasi-periodic orbits....
AbstractWe study the problem of exponentially small splitting of separatrices of one degree of freed...
In this paper, results concerning the phenomenon of adiabatic trapping into resonance for a class of...
Melnikov’s method is applied to the planar double pendulum proving it to be a chaotic system. The pa...
Cornerstone models of physics, from the semi-classical mechanics in atomic and molecular physics to ...
Adiabatic invariants for dynamical systems with one degree of freedom are derived. The method develo...