Rigorous bounds on the fast dynamo growth rate involving topological entropy

DOI10.1007/BF02101659zbMath0901.76096OpenAlexW2015464546MaRDI QIDQ1907966

Lai-Sang Young, Isaac Klapper

Publication date: 6 March 1996

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02101659

zbMATH Keywords

upper boundoperator splittinglower boundrandom mapsanti-dynamo theorem

Mathematics Subject Classification ID

Magnetohydrodynamics and electrohydrodynamics (76W05) Applications of dynamical systems (37N99)

Related Items

Stretching and alignment in chaotic and turbulent flows, Dynamo properties of the turbulent velocity field of a saturated dynamo, Convection-driven kinematic dynamos with a self-consistent shear flow, Dynamical systems and topology of magnetic fields in conducting medium, Saddle-type solenoidal basis sets, A computer-assisted proof of dynamo growth in the stretch-fold-shear map, Parallel-in-time integration of kinematic dynamos, Some rigorous results for the kinematic dynamo problem with general boundary conditions, The role of helicity and stretching in forced kinematic dynamos in a spherical shell, Optimal kinematic dynamos in a sphere, The turbulent dynamo, Dissipation of Kinetic Energy in a Magnetic Dynamo, A nonlinear dynamo driven by rapidly rotating convection, Dynamo action in flows with cat's eyes, Nonlinear dynamo action in hydrodynamic instabilities driven by shear, Spatially-periodic steady solutions to the three-dimensional Navier-Stokes equation with the \(ABC\)-force, Advected fields in maps. I: Magnetic flux growth in the stretch-fold-shear map, The α-effect in 2D fast dynamos, ABC flows then and now, Dynamo action in the ABC flows using symmetries

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On the role of stagnation points and periodic particle paths in a two-dimensional pulsed flow fast dynamo model
• Volume growth and entropy
• Lyapunov exponents, entropy and periodic orbits for diffeomorphisms
• Fast dynamo action in a steady flow
• Entropy and volume
• Chaotic flows and fast magnetic dynamos
• Fast dynamo action in the Ponomarenko dynamo
• An inequality for the entropy of differentiable maps
• Magnetic field intermittency and fast dynamo action in random helical flows
• A study of fast dynamo action in chaotic helical cells
• FAMILIES OF INVARIANT MANIFOLDS CORRESPONDING TO NONZERO CHARACTERISTIC EXPONENTS
• Shadowing and the diffusionless limit in fast dynamo theory
• Towards a realistic fast dynamo: models based on cat maps and pseudo-Anosov maps
• Construction of fast dynamos using unsteady flows and maps in three dimensions
• Magnetic field generation by the motion of a highly conducting fluid
• Topological Entropy
• Entropy for Group Endomorphisms and Homogeneous Spaces