Related papers: Dynamics near Resonance Junctions in Hamiltonian S…
For typical perturbations of convex integrable Hamiltonian system with three degrees of freedom, a path of diffusion is established to cross strong double resonant point. Together with the uniform hyperbolicity of invariant cylinders got in…
We consider models given by Hamiltonians of the form $$H(I,\phi,p,q,t;\epsilon) = h(I) + \sum_{j = 1}^n \pm(\frac{1}{2} p_j^2 + V_j(q_j)) + \epsilon Q(I,\phi,p,q,t;\epsilon)$$ where $I,\phi$ are d-dimensional actions and angles, $p,q$ are…
We consider semi-excited resonances created by a periodic orbit of hyperbolic type for Schr\"odinger type operators with a small "Planck constant". They are defined within an analytic framework based on the semi-classical quantization of…
We study dynamical evolution of a resonant triple system formed by an inner EMRI and an additional outer MBH. The relevant resonant state (\lambda_2-\varpi_1 ~ const) is supported by the relativistic apsidal precession of the inner EMRI,…
We study persistence of periodic and homoclinic orbits, first integrals and commutative vector fields in dynamical systems depending on a small parameter $\varepsilon>0$ and give several necessary conditions for their persistence. Here we…
For a class of flows on polytopes, including many examples from Evolutionary Game Theory, we describe a piecewise linear model which encapsulates the asymptotic dynamics along the heteroclinic network formed out of the polytope's vertexes…
Orbital resonances play an important role in the dynamics of planetary systems. Classical theoretical analyses found in textbooks report that libration widths of first order mean motion resonances diverge for nearly circular orbits. Here we…
In ballistic open quantum systems one often observes that the resonances in the complex-energy plane form a clear chain structure. Taking the open 3-disk system as a paradigmatic model system, we investigate how this chain structure is…
The motion of oscillatory-like nonlinear Hamiltonian systems, driven by a weak noise, is considered. A general method to find regions of stability in the phase space of a randomly-driven system, based on a specific Poincar\'e map, is…
Two-degree-of-freedom Hamiltonian systems with an elliptic equilibrium at the origin are characterised by the frequencies of the linearisation. Considering the frequencies as parameters, the system undergoes a bifurcation when the…
We use perturbation theory and bifurcation theory to analyze the dynamical behavior of resonances, associated to a model describing a particle moving within a ring around a celestial object. The central body is modeled as a homogeneous…
We consider multiscale Hamiltonian systems in which harmonic oscillators with several high frequencies are coupled to a slow system. It is shown that the oscillatory energy is nearly preserved over long times eps^{-N} for arbitrary N>1,…
A resonant chain may be formed in a multi-planetary system when ratios of the orbital periods can be expressed as ratios of small integers $T_1:T_2: \cdots :T_N=k_1: k_2: \cdots: k_N$. We investigate the dynamics and possible formation of…
We investigate numerically and experimentally dynamical systems having three interacting frequencies: a discrete mapping (a circle map), an exactly solvable model (a system of coupled ordinary differential equations), and an experimental…
Symmetries are ubiquitous in a wide range of nonlinear systems. Particularly in systems whose dynamics are determined by a Lagrangian or Hamiltonian function. For hybrid systems which possess a continuous-time dynamics determined by a…
We show the existence of drifting orbits for certain perturbations of non-convex Hamiltonian systems with several degrees of freedom. These orbits remain in the vicinity of resonant surfaces where the action variables can undergo changes…
Revivals of the coherent states of a deformed, adiabatically and cyclically varying oscillator Hamiltonian are examined. The revival time distribution is exactly that of Poincar\'{e} recurrences for a rotation map: only three distinct…
Compact objects evolving in an astrophysical environment experience a gravitational drag force known as dynamical friction. We present a multipole-frequency decomposition to evaluate the orbit-averaged energy and angular momentum…
Near-integrability is usually associated with smooth small perturbations of smooth integrable systems. Studying integrable mechanical Hamiltonian flows with impacts that respect the symmetries of the integrable structure provides an…
Stability of Hilda Asteroids in the solar system around the 3:2 resonance point is analyzed in terms of the Sun-Jupiter-asteroid elliptic restricted three-body problem. We show that the Hamiltonian of the system is well-approximated by a…