This book offers a self-contained introduction to the theory of guiding functions methods, which can be used to study the existence of periodic solutions and their bifurcations in ordinary differential equations, differential inclusions and in control theory.
Bifurcation theory is the study of small solutions of nonlinear equations, depending on a number of parameters, when for certain values of these parameters more than one solution may appear. Because of the difficulties encountered in obtaining explicit solutions to such problems…
The historical process is constructed to be a superprocess which is enriched so as to contain information on genealogy. This process together with a representation for the associated Palm measures are used to describe the modulus of continuity and equilibrium structure for a cla…
Part I. We consider dynamical systems depending on parameters in various, both conservative and dissipative settings. For such systems integrability is defined as equivariance with respect to an appropriate torus action. Part II. We consider nearly integrable families of dissip…
