Paulo Varandas
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Previous Organizations / Institutes
The organizations / institutes from the scholar's other articles in the past ten years
Research Subjects
Paulo Varandas has a total of 83 co-authors. Here are the top co-authors by number of shared publications:
- Maria Carvalho
Faculdade de Ciências da Universidade do Porto
19 shared publications - Fagner Bernardini Rodrigues
Departamento de Matemática, Universidade Federal do Rio Grande do Sul, Porto Alegre, Brazil
15 shared publications - Jorge Rocha
Departamento de Matemática, Universidade do Porto, Rua do Campo Alegre, 687, 4169-007 Porto, Portugal
11 shared publications - Mário Bessa
Universidade Aberta
11 shared publications - Thiago Bomfim
Departamento de Matemática, Universidade Federal da Bahia, Salvador, Brazil
10 shared publications - Vitor Araujo
Instituto de Matemática e Estatística, Universidade Federal da Bahia, Salvador, Brazil
7 shared publications
Latest Publications
- 27 August 2025
- Published by Elsevier in Journal of Differential Equations
- Vol. 448
Abundance of periodic orbits for typical impulsive semiflows
- 27 August 2025
- Published by Elsevier in Journal of Differential Equations
- Vol. 448
Abundance of periodic orbits for typical impulsive semiflows
- 27 July 2025
- Published by European Mathematical Society - EMS - Publishing House GmbH in Groups, Geometry, and Dynamics
Variational principles for finitely generated pseudogroup actions
We study the thermodynamic formalism of finitely generated pseudogroups acting on compact metric spaces. We introduce the notions of topological and measure-theoretical pressures for those actions, which may not admit invariant measures. Moreover, we prove a variational principle and discuss the impact of the existence of a G -homogeneous probability measure. To clarify the scope of our main results and the relevance of our approach, we address several examples and list a few applications of interest.
- 27 July 2025
- Published by European Mathematical Society - EMS - Publishing House GmbH in Groups, Geometry, and Dynamics
Variational principles for finitely generated pseudogroup actions
We study the thermodynamic formalism of finitely generated pseudogroups acting on compact metric spaces. We introduce the notions of topological and measure-theoretical pressures for those actions, which may not admit invariant measures. Moreover, we prove a variational principle and discuss the impact of the existence of a G -homogeneous probability measure. To clarify the scope of our main results and the relevance of our approach, we address several examples and list a few applications of interest.
- Open Access
Length averages for codimension one foliations
In this paper we study geometrical and dynamical properties of codimension one foliations, by exploring a relation between length averages and ball averages of certain group actions. We introduce a new mechanism, which relies on the group structure itself, to obtain irregular behavior of ball averages for certain non-amenable group actions. Several geometric realization results show that any such groups can appear connected with the topology of leaves which are connected sums of plugs with a special geometry, namely nearly equidistant boundary components. This is used to produce the first examples of codimension one $\mathcal C^\infty$ regular foliations on a compact Riemannian manifold $M$ for which the length average of some continuous function does not exist on a non-empty open subset of $M$.Open AccessLength averages for codimension one foliations
In this paper we study geometrical and dynamical properties of codimension one foliations, by exploring a relation between length averages and ball averages of certain group actions. We introduce a new mechanism, which relies on the group structure itself, to obtain irregular behavior of ball averages for certain non-amenable group actions. Several geometric realization results show that any such groups can appear connected with the topology of leaves which are connected sums of plugs with a special geometry, namely nearly equidistant boundary components. This is used to produce the first examples of codimension one $\mathcal C^\infty$ regular foliations on a compact Riemannian manifold $M$ for which the length average of some continuous function does not exist on a non-empty open subset of $M$. - Open Access
- 1 November 2024
- Published by Cambridge University Press (CUP) in Mathematical Proceedings of the Cambridge Philosophical Society
- Vol. 177 (3) , 525-551
Topological and metric emergence of continuous maps
We prove that every homeomorphism of a compact manifold with dimension one has zero topological emergence, whereas in dimension greater than one the topological emergence of a $C^0-$ generic homeomorphism is maximal, equal to the dimension of the manifold. We also show that the metric emergence of a continuous self-map on compact metric space has the intermediate value property.- 1 November 2024
- Published by Cambridge University Press (CUP) in Mathematical Proceedings of the Cambridge Philosophical Society
- Vol. 177 (3) , 525-551
Open AccessTopological and metric emergence of continuous maps
We prove that every homeomorphism of a compact manifold with dimension one has zero topological emergence, whereas in dimension greater than one the topological emergence of a $C^0-$ generic homeomorphism is maximal, equal to the dimension of the manifold. We also show that the metric emergence of a continuous self-map on compact metric space has the intermediate value property. - Open Access
- 28 October 2024
- Published by Springer Nature in Israel Journal of Mathematics
- Vol. 265 (2) , 729-768
Shape and stability of rotation sets for incompressible flows on the torus
In this paper we introduce the concept of rotation cones, determined by rotation sets, and use these to describe the stability of rotation sets of incompressible and fixed-point free continuous flows on the torus $$\mathbb{T}^{d}$$ , d ⩾ 2. The previous concept is equivalent and extends the stability of rotation numbers (and rotation vectors) in the special case of fixed-point free continuous flows on $$\mathbb{T}^{2}$$ . We prove that incompressible Lipschitz vector fields with stable rotation sets have convex rotation cones with non-empty interior, and that all extremal edges are collinear with vectors in ℤ d . If, in addition, the rotation cones are proper, then these are polyhedral with finitely many edges. Finally we prove that the set of vector fields with stable rotation sets is C 0-open and dense among those having proper rotation cones.- 28 October 2024
- Published by Springer Nature in Israel Journal of Mathematics
- Vol. 265 (2) , 729-768
Open AccessShape and stability of rotation sets for incompressible flows on the torus
In this paper we introduce the concept of rotation cones, determined by rotation sets, and use these to describe the stability of rotation sets of incompressible and fixed-point free continuous flows on the torus $$\mathbb{T}^{d}$$ , d ⩾ 2. The previous concept is equivalent and extends the stability of rotation numbers (and rotation vectors) in the special case of fixed-point free continuous flows on $$\mathbb{T}^{2}$$ . We prove that incompressible Lipschitz vector fields with stable rotation sets have convex rotation cones with non-empty interior, and that all extremal edges are collinear with vectors in ℤ d . If, in addition, the rotation cones are proper, then these are polyhedral with finitely many edges. Finally we prove that the set of vector fields with stable rotation sets is C 0-open and dense among those having proper rotation cones. - Open Access
Shift operators and their classification
We introduce a class of linear bounded invertible operators on Banach spaces, called shift operators, which comprises weighted backward shifts and models finite products of weighted backward shifts and dissipative composition operators. We classify vast families of these shift operators, including the ones generated by orthogonal, diagonalizable, rotation or hyperbolic matrices. and this classification yields verifiable conditions which we use to construct concrete examples of shift operators with a variety of dynamical properties. As a consequence, we show that, for large classes of shift operators, generalized hyperbolicity is equivalent to the shadowing property.
Open AccessShift operators and their classification
We introduce a class of linear bounded invertible operators on Banach spaces, called shift operators, which comprises weighted backward shifts and models finite products of weighted backward shifts and dissipative composition operators. We classify vast families of these shift operators, including the ones generated by orthogonal, diagonalizable, rotation or hyperbolic matrices. and this classification yields verifiable conditions which we use to construct concrete examples of shift operators with a variety of dynamical properties. As a consequence, we show that, for large classes of shift operators, generalized hyperbolicity is equivalent to the shadowing property.
- 3 June 2024
- Published by Springer Nature in Bulletin of the Brazilian Mathematical Society, New Series
- Vol. 55 (3) , 1-19
Phase Transitions for Surface Diffeomorphisms
- 3 June 2024
- Published by Springer Nature in Bulletin of the Brazilian Mathematical Society, New Series
- Vol. 55 (3) , 1-19
Phase Transitions for Surface Diffeomorphisms
- 27 May 2024
- Published by Elsevier in Journal of Mathematical Analysis and Applications
- Vol. 539 (2)
Discrete symmetries of smooth flows and their time-t maps
- 27 May 2024
- Published by Elsevier in Journal of Mathematical Analysis and Applications
- Vol. 539 (2)
Discrete symmetries of smooth flows and their time-t maps
- 15 May 2024
- Published by Elsevier in Journal of Mathematical Analysis and Applications
- Vol. 539 (1)
Regularity of the Hausdorff dimension of some hyperbolic systems
- 15 May 2024
- Published by Elsevier in Journal of Mathematical Analysis and Applications
- Vol. 539 (1)
Regularity of the Hausdorff dimension of some hyperbolic systems
- Open Access
Abundance of periodic orbits for typical impulsive flows
Impulsive dynamical systems, modeled by a continuous semiflow and an impulse function, may be discontinuous and may have non-intuitive topological properties, as the non-invariance of the non-wandering set or the non-existence of invariant probability measures. In this paper we study dynamical features of impulsive flows parameterized by the space of impulses. We prove that impulsive semiflows determined by a C1-Baire generic impulse are such that the set of hyperbolic periodic orbits is dense in the set of non-wandering points which meet the impulsive region. As a consequence, we provide sufficient conditions for the non-wandering set of a typical impulsive semiflow (except the discontinuity set) to be invariant. Several applications are given concerning impulsive semiflows obtained from billiard, Anosov and geometric Lorenz flows.
Open AccessAbundance of periodic orbits for typical impulsive flows
Impulsive dynamical systems, modeled by a continuous semiflow and an impulse function, may be discontinuous and may have non-intuitive topological properties, as the non-invariance of the non-wandering set or the non-existence of invariant probability measures. In this paper we study dynamical features of impulsive flows parameterized by the space of impulses. We prove that impulsive semiflows determined by a C1-Baire generic impulse are such that the set of hyperbolic periodic orbits is dense in the set of non-wandering points which meet the impulsive region. As a consequence, we provide sufficient conditions for the non-wandering set of a typical impulsive semiflow (except the discontinuity set) to be invariant. Several applications are given concerning impulsive semiflows obtained from billiard, Anosov and geometric Lorenz flows.