Related papers: Emergence of Multi-Scroll Attractors
The well known butterfly effect got its nomenclature from its two wings geometrical structure in phase space. There are chaotic dynamics from simple one-wing to multiple-wings complex structures in phase space. In this communication we…
This paper is a review of results which have been recently obtained by applying mathematical concepts drawn, in particular, from differential geometry and topology, to the physics of Hamiltonian dynamical systems with many degrees of…
Turbulent flows present rich dynamics originating from non-trivial energy fluxes across scales, non-stationary forcings and geometrical constraints. This complexity manifests in non-hyperbolic chaos, randomness, state-dependent persistence…
We discuss recent work with E.Floratos (JHEP 1004:036,2010) on Nambu Dynamics of Intersecting Surfaces underlying Dissipative Chaos in $R^{3}$. We present our argument for the well studied Lorenz and R\"{o}ssler strange attractors. We…
We extend the framework of Nambu-Hamiltonian Mechanics to include dissipation in $R^{3}$ phase space. We demonstrate that it accommodates the phase space dynamics of low dimensional dissipative systems such as the much studied Lorenz and…
In Hamiltonian mechanics, a (continuous) symmetry leads to conserved quantity, which is a function on (extended) phase space. In Nambu mechanics, a straightforward consequence of symmetry is just a relative integral invariant, a…
Turbulent-laminar patterns are ubiquitous near transition in wall-bounded shear flows. Despite recent progress in describing their dynamics in analogy to non-equilibrium phase transitions, there is no theory explaining their emergence.…
The phase space of a typical Hamiltonian system contains both chaotic and regular orbits, mixed in a complex, fractal pattern. One oft-studied phenomenon is the algebraic decay of correlations and recurrence time distributions. For…
The aim of this work is to establish the existence of invariant manifolds in complex systems. Considering trajectory curves integral of multiple time scales dynamical systems of dimension two and three (predator-prey models, neuronal…
Material elements - which are lines, surfaces, or volumes behaving as passive, non-diffusive markers - provide an inherently geometric window into the intricate dynamics of chaotic flows. Their stretching and folding dynamics has immediate…
There exists a variety of physically interesting situations described by continuous maps that are nondifferentiable on some surface in phase space. Such systems exhibit novel types of bifurcations in which multiple coexisting attractors can…
Starting with the generally well accepted opinion that quantizing an arbitrary Hamiltonian system involves picking out some additional structure on the classical phase space (the {\sl shadow} of quantum mechanics in the classical theory),…
We have revealed that the barrier-tunneling process in non-integrable systems is strongly linked to chaos in complex phase space by investigating a simple scattering map model. The semiclassical wavefunction reproduces complicated features…
Zonal jets are striking and beautiful examples of the propensity for geophysical turbulent flows to spontaneously self-organize into robust, large scale coherent structures. There exist many dynamical mechanisms for the formation of zonal…
Much has been learned about string theory over the last few years by studying properties of cycles and branes in a given background geometry. Here we discuss three situations (quantum volume, attractor flows/D-brane stability, and dynamical…
Chaotic attractors commonly contain periodic solutions with unstable manifolds of different dimensions. This allows for a zoo of dynamical phenomena not possible for hyperbolic attractors. The purpose of this Letter is to demonstrate these…
Some dynamical properties present in a problem concerning the acceleration of particles in a wave packet are studied. The dynamics of the model is described in terms of a two-dimensional area preserving map. We show that the phase space is…
We study chaotic dynamics in a system of four differential equations describing the dynamics of five identical globally coupled phase oscillators with biharmonic coupling. We show that this system exhibits strange spiral attractors…
Following the Nambu mechanics framework we demonstrate that the non-dissipative part of the Lorenz system can be generated by the intersection of two quadratic surfaces that form a doublet under the group SL(2,R). All manifolds are…
Nambu mechanics is a generalized Hamiltonian dynamics characterized by an extended phase space and multiple Hamiltonians. In a previous paper [Prog. Theor. Exp. Phys. 2013, 073A01 (2013)] we revealed that the Nambu mechanical structure is…