12 citations · 14 across the 4 of their papers we have counts for
9 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…
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_{…
Meanders, zero numbers and the cell structure of Sturm global attractors
Carlos Rocha, Bernold Fiedler
We study global attractors of semiflows generated by semilinear partial parabolic differential equations of the form ,…
Boundary orders and geometry of the signed Thom-Smale complex for Sturm global attractors
Bernold Fiedler, Carlos Rocha
We embark on a detailed analysis of the close relations between combinatorial and geometric aspects of the scalar parabolic PDE \begin{equation}\label{eq:*} u_t = u_{xx} + f(x,u,u_…
An explicit Lyapunov function for reflection symmetric parabolic partial differential equations on the circle
Bernold Fiedler, Clodoaldo Grotta-Ragazzo, Carlos Rocha
We construct an explicit Lyapunov function for scalar parabolic reaction-advection-diffusion equations under periodic boundary conditions. We assume the nonlinearity is even in the…
Sturm 3-ball global attractors 3: Examples of Thom-Smale complexes
Bernold Fiedler, Carlos Rocha
Examples complete our trilogy on the geometric and combinatorial characterization of global Sturm attractors which consist of a single closed 3-ball. The underlying s…
Sturm 3-ball global attractors 2: Design of Thom-Smale complexes
Bernold Fiedler, Carlos Rocha
This is the second of three papers on the geometric and combinatorial characterization of global Sturm attractors which consist of a single closed 3-ball. The underlying scalar PDE…
Sturm 3-ball global attractors 1: Thom-Smale complexes and meanders
Bernold Fiedler, Carlos Rocha
This is the first of three papers on the geometric and combinatorial characterization of global Sturm attractors which consist of a single closed 3-ball. The underlying scalar PDE…