Complexified Dynamical Systems
arXiv:0705.3893 · doi:10.1088/1751-8113/40/32/F02
Abstract
Many dynamical systems, such as the Lotka-Volterra predator-prey model and the Euler equations for the free rotation of a rigid body, are PT symmetric. The standard and well-known real solutions to such dynamical systems constitute an infinitessimal subclass of the full set of complex solutions. This paper examines a subset of the complex solutions that contains the real solutions, namely, those having PT symmetry. The condition of PT symmetry selects out complex solutions that are periodic.
13 pages, 12 figures, to appear in Fast Track Communications, Journal of Physics A: Mathematical and Theoretical
References in corpus (13)
- Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry
- An integrable shallow water equation with peaked solitons
- Complex Extension of Quantum Mechanics
- PT-Symmetric Quantum Mechanics
- Spectral equivalences, Bethe Ansatz equations, and reality properties in PT-symmetric quantum mechanics
- Introduction to PT-Symmetric Quantum Theory
- Must a Hamiltonian be Hermitian?
- Supersymmetry and the spontaneous breakdown of PT symmetry
- Scalar Quantum Field Theory with Cubic Interaction
- PT-Symmetric Extension of the Korteweg-de Vries Equation
- Classical Trajectories for Complex Hamiltonians
- Complex Trajectories of a Simple Pendulum
- Spontaneous Breaking of Classical PT Symmetry
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- Non-Hermitian Physics
- Pseudo-Hermitian Representation of Quantum Mechanics
- Gain-Driven Discrete Breathers in PT-Symmetric Nonlinear Metamaterials
- Complex Worldline Instantons and Quantum Interference in Vacuum Pair Production
- Classical limit of non-Hermitian quantum dynamics - a generalised canonical structure
- Complex Correspondence Principle
- Integrable nonlocal asymptotic reductions of physically significant nonlinear equations
- Quantum effects in classical systems having complex energy
- Bohmian quantum trajectories from coherent states
- Chaotic systems in complex phase space
- Classical and quantum dynamics in the (non-Hermitian) Swanson oscillator
- PT-symmetry breaking in complex nonlinear wave equations and their deformations
- Quantum tunneling as a classical anomaly
- Probability Density in the Complex Plane
- Synchrony for weak coupling in the complexified Kuramoto model
- Brouwer's problem on a heavy particle in a rotating vessel: wave propagation, ion traps, and rotor dynamics
- Exact Isospectral Pairs of PT-Symmetric Hamiltonians
- Classical oscillator with position-dependent mass in a complex domain
- Periodic orbits for classical particles having complex energy
- Conduction bands in classical periodic potentials
- Does the complex deformation of the Riemann equation exhibit shocks?
- Dynamical Systems and Poisson Structures
- Complex Trajectories in a Classical Periodic Potential
- Complexified Synchrony
- PT Symmetric Schrödinger Operators: Reality of the Perturbed Eigenvalues
- PT-symmetrically deformed shock waves
- PT-symmetry in quasi-integrable models
- PT-Symmetric Model of Immune Response
- Effects of complex parameters on classical trajectories of Hamiltonian systems