107 citations · 814 across the 36 of their papers we have counts for
20 papers · 1 filter
Perturbation theory for the Fokker-Planck operator in chaos
Jeffrey M. Heninger, Domenico Lippolis, Predrag Cvitanovic
The stationary distribution of a fully chaotic system typically exhibits a fractal structure, which dramatically changes if the dynamical equations are even slightly modified. Pert…
Unstable manifolds of relative periodic orbits in the symmetry-reduced state space of the Kuramoto-Sivashinsky system
Nazmi Burak Budanur, Predrag Cvitanović
Systems such as fluid flows in channels and pipes or the complex Ginzburg-Landau system, defined over periodic domains, exhibit both continuous symmetries, translational and rotati…
Neighborhoods of periodic orbits and the stationary distribution of a noisy chaotic system
Jeffrey M. Heninger, Domenico Lippolis, Predrag Cvitanovic
The finest state space resolution that can be achieved in a physical dynamical system is limited by the presence of noise. In the weak-noise approximation the neighborhoods of dete…
Periodic orbit analysis of a system with continuous symmetry - a tutorial
Nazmi Burak Budanur, Daniel Borrero-Echeverry, Predrag Cvitanović
Dynamical systems with translational or rotational symmetry arise frequently in studies of spatially extended physical systems, such as Navier-Stokes flows on periodic domains. In…
Periodic eigendecomposition and its application to Kuramoto-Sivashinsky system
Xiong Ding, Predrag Cvitanović
Periodic eigendecomposition, to be formulated in this paper, is a numerical method to compute Floquet spectrum and Floquet vectors along periodic orbits in a dynamical system. It i…
Reduction of SO(2) symmetry for spatially extended dynamical systems
Nazmi Burak Budanur, Predrag Cvitanović, Ruslan L. Davidchack +1
Spatially extended systems, such as channel or pipe flows, are often equivariant under continuous symmetry transformations, with each state of the flow having an infinite number of…
Cartography of high-dimensional flows: A visual guide to sections and slices
Predrag Cvitanovic, Daniel Borrero-Echeverry, Keith M. Carroll +2
Symmetry reduction by the method of slices quotients the continuous symmetries of chaotic flows by replacing the original state space by a set of charts, each covering a neighborho…
Knowing when to stop: how noise frees us from determinism
Predrag Cvitanovic, Domenico Lippolis
Deterministic chaotic dynamics presumes that the state space can be partitioned arbitrarily finely. In a physical system, the inevitable presence of some noise sets a finite limit…
Reduction of continuous symmetries of chaotic flows by the method of slices
Stefan Froehlich, Predrag Cvitanovic
We study continuous symmetry reduction of dynamical systems by the method of slices (method of moving frames) and show that a `slice' defined by minimizing the distance to a single…
Continuous symmetry reduction and return maps for high-dimensional flows
Evangelos Siminos, Predrag Cvitanović
We present two continuous symmetry reduction methods for reducing high-dimensional dissipative flows to local return maps. In the Hilbert polynomial basis approach, the equivariant…
How well can one resolve the state space of a chaotic map?
Domenico Lippolis, Predrag Cvitanovic
All physical systems are affected by some noise that limits the resolution that can be attained in partitioning their state space. For chaotic, locally hyperbolic flows, this resol…
On the state space geometry of the Kuramoto-Sivashinsky flow in a periodic domain
Predrag Cvitanović, Ruslan L. Davidchack, Evangelos Siminos
The continuous and discrete symmetries of the Kuramoto-Sivashinsky system restricted to a spatially periodic domain play a prominent role in shaping the invariant sets of its chaot…
Periodic orbits in scattering from elastic voids
Niels Sondergaard, Predrag Cvitanovic, Andreas Wirzba
The scattering determinant for the scattering of waves from several obstacles is considered in the case of elastic solids with voids. The multi-scattering determinant displays cont…
Variational method for locating invariant tori
Yueheng Lan, Cristel Chandre, Predrag Cvitanovic
We formulate a variational fictitious-time flow which drives an initial guess torus to a torus invariant under given dynamics. The method is general and applies in principle to con…
Variational method for finding periodic orbits in a general flow
Yueheng Lan, Predrag Cvitanovic
A variational principle for determining unstable periodic orbits of flows as well as unstable spatio-temporally periodic solutions of extended systems is proposed and implemented.…
Turbulent fields and their recurrences
Predrag Cvitanovic, Yueheng Lan
We introduce a new variational method for finding periodic orbits of flows and spatio-temporally periodic solutions of classical field theories, a generalization of the Newton meth…
A Perturbative Analysis of Modulated Amplitude Waves in Bose-Einstein Condensates
Mason A. Porter, Predrag Cvitanovic'
We apply Lindstedt's method and multiple scale perturbation theory to analyze spatio-temporal structures in nonlinear Schrödinger equations and thereby study the dynamics of quasi-…
Modulated Amplitude Waves in Bose-Einstein Condensates
Mason A. Porter, Predrag Cvitanovic
We analyze spatio-temporal structures in the Gross-Pitaevskii equation to study the dynamics of quasi-one-dimensional Bose-Einstein condensates (BECs) with mean-field interactions.…
Wave Chaos in Elastodynamic Cavity Scattering
Andreas Wirzba, Niels Sondergaard, Predrag Cvitanovic
The exact elastodynamic scattering theory is constructed to describe the spectral properties of two- and more-cylindrical cavity systems, and compared to an elastodynamic generaliz…
Chaotic Field Theory - a Sketch
Predrag Cvitanovic
Spatio-temporally chaotic dynamics of a classical field can be described by means of an infinite hierarchy of its unstable spatio-temporally periodic solutions. The periodic orbit…