Related papers: Nodal points and the transition from ordered to ch…
We study main bifurcations of multidimensional diffeomorphisms having a non-transversal homoclinic orbit to a saddle-node fixed point. On a parameter plane we build a bifurcation diagram for single-round periodic orbits lying entirely in a…
Invariant manifolds are the skeleton of the chaotic dynamics in Hamiltonian systems. In Celestial Mechanics, for instance, these geometrical structures are applied to a multitude of physical and practical problems, such as to the…
We investigate the transition from integrable to chaotic dynamics in the quantum mechanical wave functions from the point of view of the nodal structure by employing a two dimensional quartic oscillator. We find that the number of nodal…
A chaos control algorithm is developed to actively stabilize unstable periodic orbits of higher-dimensional systems. The method assumes knowledge of the model equations and a small number of experimentally accessible parameters. General…
In the present work we consider a diatomic granular crystal, consisting of alternating aluminum and steel spheres, where the first sphere is an aluminum one. The combination of dissipation, driving of the boundary, and intrinsic…
A Lorenz-like model was set up recently, to study the hydrodynamic instabilities in a driven active matter system. This Lorenz model differs from the standard one in that all three equations contain non-linear terms. The additional…
Equilibrium phase transitions may be defined as nonanalytic points of thermodynamic functions, e.g., of the canonical free energy. Given a certain physical system, it is of interest to understand which properties of the system account for…
In recent years, analysis and control of quantum chaos are increasingly important, but the lack of the concept of trajectory makes it impossible to analyze quantum chaos by the methods used in classical chaos. This research aims to connect…
Under certain symmetries, degenerate points in three-dimensional metals form one-dimensional nodal lines. These nodal lines sometimes exhibit intricate knotted structures and have been studied in various contexts. As one of the most common…
We study a homoclinic flip bifurcation of case~\textbf{C}, where a homoclinic orbit to a saddle equilibrium with real eigenvalues changes from being orientable to nonorientable. This bifurcation is of codimension two, and it is the lowest…
We review the occurrence of the patterns of the onset of chaos in low-dimensional nonlinear dissipative systems in leading topics of condensed matter physics and complex systems of various disciplines. We consider the dynamics associated…
The order from quantum disorder (OFQD) phenomenon was first discovered in quantum spin systems in geometric frustrated lattice. Similar phenomenon was also discovered in interacting bosonic systems or quantum spin systems with spin-orbit…
We use a free-energy minimization approach to describe the secular and dynamical instabilities as well as the bifurcations along equilibrium sequences of rotating, self-gravitating fluid systems. Our approach is fully nonlinear and stems…
In a 2D conservative Hamiltonian system there is a formal integral $\Phi$ besides the energy H. This is not convergent near a stable periodic orbit, but it is convergent near an unstable periodic orbit. We explain this difference and we…
A phase transition is an example of a ``topological defect'' in the space of parameters of a quantum or classical many-body systems. In this paper, we consider phase diagram topological defects of higher codimension. These have the property…
In atomic nuclei, ordered and chaotic states generally coexist. In this paper the transition from ordered to chaotic states will be discussed in the framework of roto-vibrational and shell models. In particular for $^{160}Gd$, in the…
Topology is being widely adopted to understand and to categorize quantum matter in modern physics. The nexus of topology orders, which engenders distinct quantum phases with benefits to both fundamental research and practical applications…
The dynamics of a general Bianchi IX model with three scale factors is examined. The matter content of the model is assumed to be comoving dust plus a positive cosmological constant. The model presents a critical point of…
We present an experimental study of quasiperiodic transitions between a highly ordered square-lattice pattern and a disordered, defect-riddled state, in a circular Faraday system. We show that the transition is driven initially by a…
Mixed-order phase transitions display a discontinuity in the order parameter like first-order transitions yet feature critical behavior like second-order transitions. Such transitions have been predicted for a broad range of equilibrium and…