174 citations · 341 across the 19 of their papers we have counts for
26 papers
Counting Hamiltonian Sturm permutations: generating functions and Gaussian distributions
Bernold Fiedler, Carlos Rocha
Our combinatorial analysis is motivated by the PDE dynamics \begin{equation} \mathbf{u_t} = \mathbf{u_{xx}} + \mathbf{g}(\mathbf{u}),\qquad 0<\mathbf{x}<1, \end{equation} of soluti…
Classification of global attractors for -equivariant parabolic equations: a survey
Carlos Rocha, Bernold Fiedler, Alejandro López-Nieto
We survey the global dynamics of semiflows generated by scalar semilinear parabolic equations which are equivariant under spatial shifts of $x\in \mathbb{S}^1=\mat…
Scalar polynomial vector fields in real and complex time
Bernold Fiedler
In the present paper, the simplest scalar ODE case is studied for polynomials of degree with simple complex zeros. The…
Real chaos and complex time
Bernold Fiedler
Real vector fields in extend to , for complex entire . One known consequence are exponentially small upper bounds \begin{equation*}…
Design of Sturm global attractors 2: Time-reversible Chafee-Infante lattices of 3-nose meanders
Bernold Fiedler, Carlos Rocha
This sequel continues our exploration arxiv:2302.12531 of a deceptively ``simple'' class of global attractors, called Sturm due to nodal properties. They arise for the semilinear s…
Design of Sturm global attractors 1: Meanders with three noses, and reversibility
Bernold Fiedler, Carlos Rocha
We systematically explore a simple class of global attractors, called Sturm due to nodal properties, for the semilinear scalar parabolic PDE \begin{equation*}\label{eq:*} u_t = u_{…