A gap mapping is a discontinuous interval mapping with two strictly increasing branches that have... more A gap mapping is a discontinuous interval mapping with two strictly increasing branches that have a gap between their ranges. They are one-dimensional dynamical systems, which arise in the study of certain higher dimensional flows, for example the Lorenz flow and the Cherry flow. In this paper, we prove hyperbolicity of renormalization acting on $C^3$ dissipative gap mappings, and show that the topological conjugacy classes of infinitely renormalizable gap mappings are $C^1$ manifolds.
Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 2020
We classify the global phase portraits in the Poincaré disc of the quadratic polynomial Liénard d... more We classify the global phase portraits in the Poincaré disc of the quadratic polynomial Liénard differential systems \dot{x}=y, \quad \dot{y}=(ax+b)y+cx^2+dx+e, where (x, y) ∈ ℝ2 are the variables and a,b,c,d,e are real parameters.
Page 1. Renormalization operator for affine dissipative Lorenz maps Márcio Alves∗ and Eduardo Col... more Page 1. Renormalization operator for affine dissipative Lorenz maps Márcio Alves∗ and Eduardo Colli March 14, 2008 Abstract We study properties of the renormalization operator arising in a three-dimensional family of affine dissipative Lorenz maps. ...
A gap mapping is a discontinuous interval mapping with two strictly increasing branches that have... more A gap mapping is a discontinuous interval mapping with two strictly increasing branches that have a gap between their ranges. They are one-dimensional dynamical systems, which arise in the study of certain higher dimensional flows, for example the Lorenz flow and the Cherry flow. In this paper, we prove hyperbolicity of renormalization acting on $C^3$ dissipative gap mappings, and show that the topological conjugacy classes of infinitely renormalizable gap mappings are $C^1$ manifolds.
Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 2020
We classify the global phase portraits in the Poincaré disc of the quadratic polynomial Liénard d... more We classify the global phase portraits in the Poincaré disc of the quadratic polynomial Liénard differential systems \dot{x}=y, \quad \dot{y}=(ax+b)y+cx^2+dx+e, where (x, y) ∈ ℝ2 are the variables and a,b,c,d,e are real parameters.
Page 1. Renormalization operator for affine dissipative Lorenz maps Márcio Alves∗ and Eduardo Col... more Page 1. Renormalization operator for affine dissipative Lorenz maps Márcio Alves∗ and Eduardo Colli March 14, 2008 Abstract We study properties of the renormalization operator arising in a three-dimensional family of affine dissipative Lorenz maps. ...
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Papers by Marcio Gouveia