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The behavior of two pacemakers simulated by integrate and fire oscillators reciprocally connected by synapses is studied. The activation of each synapse produces a sudden potential shift in the post-synaptic neuron. Two sorts of behaviour may occur when at least one synapse is excitatory. Phase-locking occurs for almost every set of parameters, and given(More)
We study topological and ergodic properties of some almost hyperbolic diffeomorphisms on two dimensional manifolds. Under generic conditions, diffeo-morphisms obtained from Anosov by an isotopy pushing together the stable and unstable manifolds to be tangent at a fixed point, are conjugate to Anosov. For a finite codimension subset at the boundary of Anosov(More)
For continuous maps on a compact manifold M , particularly for those that do not preserve the Lebesgue measure m, we define the observable invariant measures as a generalization of the Sinai-Ruelle-Bowen (SRB) measures. We prove that any continuous map has observable measures and characterize those that are SRB in terms of the observability. We also define(More)
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