5 papers
Finite-scale geometric invariants for chaotic and weakly chaotic dynamics
Vinesh Vijayan
We introduce a finite scale geometric observable that quantifies the growth rate of localized sets under time evolution in dissipative dynamical systems. Defined at finite time and…
Universality classes of chaos in non Markovian dynamics
Vinesh Vijayan
Classical chaos theory rests on the notion of universality, whereby disparate dynamical systems share identical scaling laws. Existing universality classes, however, implicitly ass…
Universal Curvature Force on Dislocations from a Cartan Geometric Defect Action
Vinesh Vijayan, T Ishwarya, M Parveenbanu +1
We develop a unified Cartan geometric framework where dislocations and disclinations correspond to torsion and curvature of the material coframe connection, respectively, and phase…
Geometric Formulation of Combined Conservative Dissipative Mechanics via Contact Hamiltonian Dynamics Symmetries, Reduction, and Variational Integrators
Vinesh Vijayan, Pasupuleti Thejasree, P Satish Kumar +1
We develop a unified geometric framework for mechanical systems that combine conservative and dissipative dynamics by formulating them on contact manifolds. Within this setting, we…
Noise Reinstates Collapsed Populations: Stochastic Reversal of Deterministic Extinction
Vinesh Vijayan, B Priyadharshini, R Sathish Kumar +1
Conventional wisdom suggests that environmental noise drives populations toward extinction. In contrast, we report a paradoxical phenomenon in which stochasticity reverses a determ…