#### Filter Results:

#### Publication Year

2004

2010

#### Publication Type

#### Co-author

#### Publication Venue

Learn More

The dimensional reduction of D-dimensional spacetimes arising in string/M-theory, to the conformal Einstein frame, may give rise to cosmologies with accelerated expansion. Through a complete analysis of the dynamics of doubly warped product spacetimes, in terms of scale invariant variables, it is demonstrated that for D ≥ 10, eternally accelerating… (More)

- Mikael Fjällborg, J. Mark Heinzle, Claes Uggla
- 2006

We study equilibrium states in relativistic galactic dynamics which are described by stationary solutions of the Einstein-Vlasov system for collisionless matter. We recast the equations into a regular three-dimensional system of autonomous first order ordinary differential equations on a bounded state space. Based on a dynamical systems analysis we derive… (More)

- J. Mark Heinzle, Claes Uggla
- 2006

We investigate the dynamics of spatially homogeneous solutions of the Einstein-Vlasov equations with Bianchi type I symmetry by using dynamical systems methods. All models are forever expanding and isotropize toward the future; toward the past there exists a singularity. We identify and describe all possible past asymptotic states; in particular, on the… (More)

- J. Mark Heinzle, Alan D. Rendall, Claes Uggla
- 2004

We investigate spherically symmetric equilibrium states of the Vlasov-Poisson system, relevant in galactic dynamics. We recast the equations into a regular three-dimensional system of autonomous first order ordinary differential equations on a region with compact closure. Based on a dynamical systems analysis we derive theorems that guarantee that the… (More)

We consider models of accelerated cosmological expansion described by the Einstein equations coupled to a nonlinear scalar field with a suitable exponential potential. We show that homogeneous and isotropic solutions are stable under small nonlinear perturbations without any symmetry assumptions. Our proof is based on results on the nonlinear stability of… (More)

- J. Mark Heinzle, Claes Uggla
- 2009

We consider the dynamics towards the initial singularity of Bianchi type IX vacuum and orthogonal perfect fluid models with a linear equation of state. The 'Bianchi type IX attractor theorem' states that the past asymptotic behavior of generic type IX solutions is governed by Bianchi type I and II vacuum states (Mixmaster attractor). We give a comparatively… (More)

- J. Mark Heinzle, Niklas Röhr, Claes Uggla
- 2008

We investigate relativistic spherically symmetric static perfect fluid models in the framework of the theory of dynamical systems. The field equations are recast into a regular dynamical system on a 3-dimensional compact state space, thereby avoiding the non-regularity problems associated with the Tolman-Oppenheimer-Volkoff equation. The global picture of… (More)

- J. Mark Heinzle
- 2008

For spherically symmetric relativistic perfect fluid models, the well-known Buchdahl inequality provides the bound 2M/R 8/9, where R denotes the surface radius and M the total mass of a solution. By assuming that the ratio p/ρ be bounded, where p is the pressure, ρ the density of solutions, we prove a sharper inequality of the same type, which depends on… (More)

- Simone Calogero, J. Mark Heinzle
- SIAM J. Applied Dynamical Systems
- 2010

- ‹
- 1
- ›