Stable weakly shadowable volume-preserving systems are volume-hyperbolic

Quadratic Volume-preserving Maps: (un)stable Manifolds, Hyperbolic Dynamics, and Vortex-bubble Bifurcations

We implement a semi-analytic scheme for numerically computing high order polynomial approximations of the stable and unstable manifolds associated with the fixed points of the normal form for the family of quadratic volume-preserving diffeomorphisms with quadratic inverse. We use this numerical scheme to study some hyperbolic dynamics associated with an invariant structure called a vortex-bubbl...

Quadratic Volume-Preserving Maps: (Un)stable Manifolds, Hyperbolic Dynamics, and Vortex-Bubble Bifurcations

We implement a semi-analytic scheme for numerically computing high order polynomial approximations of the stable and unstable manifolds associated with the fixed points of the normal form for the family of quadratic volume-preserving diffeomorphisms with quadratic inverse. We use this numerical scheme to study some hyperbolic dynamics associated with an invariant structure called a vortex bubbl...

Adiabatic invariance in volume-preserving systems

Entropy Production in Open Volume–Preserving Systems

We describe a mechanism leading to positive entropy production in volumepreserving systems under nonequilibrium conditions. We consider volumepreserving systems sustaining a diffusion process like the multibaker map or the Lorentz gas. A continuous flux of particles is imposed across the system resulting in a stationary gradient of concentration. In the limit where such flux boundary conditions...

Approximation of Volume-preserving Homeomorphisms by Volume-preserving Diffeomorphisms

Given a volume-preserving homeomorphism of a smooth manifold of dimension n ≥ 5, we give a necessary and sufficient condition for uniform approximability by (volume-preserving) diffeomorphisms.