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- Jannie A. Leach
- 2005

In this paper we consider a cosmological Friedmann Robertson Walker brane world embedded in a 5-dimensional anti-de Sitter Schwarzschild bulk. We show, using potential diagrams, that for an anti-de Sitter bulk the null geodesics never return to the brane. Null geodesics do however return for k = +1 when we include the Schwarzschild like mass and the… (More)

- S Carloni, J A Leach, S Capozziello, S Dunsby
- 2006

We study the phase–space of FLRW models derived from Scalar– Tensor Gravity where the non–minimal coupling is F (φ) = ξφ 2 and the effective potential is V (φ) = λφ n. Our analysis allows to unfold many feature of the cosmology of this class of theories. For example, the evolution mechanism towards states indistinguishable from GR is recovered and proved to… (More)

- Jannie A Leach, Sante Carloni, Peter K S Dunsby
- 2006

We give the equations governing the shear evolution in Bianchi spacetimes for general f (R)-theories of gravity. We consider the case of R n-gravity and perform a detailed analysis of the dynamics in Bianchi I cosmologies which exhibit local rotational symmetry. We find exact solutions and study their behaviour and stability in terms of the values of the… (More)

In this paper we study the dynamics of orthogonal spatially homogeneous Bianchi cosmologies in R n-gravity. We construct a compact state space by dividing the state space into different sectors. We perform a detailed analysis of the cosmological behaviour in terms of the parameter n, determining all the equilibrium points, their stability and corresponding… (More)

- J. A. Leach, S. Shaw
- 2009

In this paper, we consider an initial-boundary value problem for the Korteweg-de Vries equation on the negative quarter-plane. The normalized Korteweg-de Vries equation considered is given by uτ + uux + uxxx = 0, x < 0, τ > 0, where x and τ represent dimensionless distance and time respectively. In particular , we consider the case when the initial and… (More)

- D. J. Needham, J. A. Leach, P. M. McCabe
- SIAM Journal of Applied Mathematics
- 1998

- D. J. Needham, J. A. Leach, P. M. McCabe
- SIAM Journal of Applied Mathematics
- 2000

- Jannie A Leach
- 2006

We give the equations governing the shear evolution in Bianchi spacetimes for general f (R)-theories of gravity. We consider the case of R n-gravity and perform a detailed analysis of the dynamics in Bianchi I cosmologies which exhibit local rotational symmetry. We find exact solutions and study their behaviour and stability in terms of the values of the… (More)

- J. A. Leach
- Appl. Math. Lett.
- 2011

In this paper we address important issues surrounding the choice of variables when performing a dynamical systems analysis of alternative theories of gravity. We discuss the advantages and disadvantages of compactifying the state space, and illustrate this using two examples. We first show how to define a compact state space for the class of LRS Bianchi… (More)