Abstract We show that in viscous approximations of functionals defined on Finsler manifolds, it is possible to construct suitable sequences critical points these satisfying the expected Morse index bounds as Lazer–Solimini’s theory, together with entropy condition Michael Struwe.

Finding multiple local minima in the merit function landscape of optical system optimization is a difficult task, especially for complex designs that have a large number of variables. We discuss here a method that enables a rapid generation of new local minima for optical systems of arbitrary complexity. We have recently shown that saddle points known in mathematics as Morse index 1 saddle poin...

We propose a new method for representing the topology and geometry of 2D compact surfaces embedded in a three-dimensional space. Topology is modeled through a skeletal graph, where a distance function is employed as a Morse function. Invariance to rigid transformations follows directly from this choice of Morse function. Geometry is captured by modeling the evolution of level curves of the dist...

We examine semilinear Neumann problems driven by the Laplacian plus an unbounded and indefinite potential. The reaction is a Carathéodory function which exhibits linear growth near ±∞. We allow for resonance to occur with respect to a nonprincipal nonnegative eigenvalue, and we prove several multiplicity results. Our approach uses critical point theory, Morse theory and the reduction method (th...

A generally applicable, automatic method for the efficient computation of a database of global dynamics of a multiparameter dynamical system is introduced. An outer approximation of the dynamics for each subset of the parameter range is computed using rigorous numerical methods and is represented by means of a directed graph. The dynamics is then decomposed into the recurrent and gradient-like ...

In this paper, two methods for constructing systems of ordinary differential equations realizing any fixed finite set of equilibria in any fixed finite dimension are introduced; no spurious equilibria are possible for either method. By using the first method, one can construct a system with the fewest number of equilibria, given a fixed set of attractors. Using a strict Lyapunov function for ea...