A Non Conventional Ergodic Theorem for a Nil-System

Non-linear ergodic theorems in complete non-positive curvature metric spaces

Hadamard (or complete $CAT(0)$) spaces are complete, non-positive curvature, metric spaces. Here, we prove a nonlinear ergodic theorem for continuous non-expansive semigroup in these spaces as well as a strong convergence theorem for the commutative case. Our results extend the standard non-linear ergodic theorems for non-expansive maps on real Hilbert spaces, to non-expansive maps on Ha...

A Mean Ergodic Theorem For Asymptotically Quasi-Nonexpansive Affine Mappings in Banach Spaces Satisfying Opial's Condition

Individual ergodic theorem for intuitionistic fuzzy observables using intuitionistic fuzzy state

The classical ergodic theory hasbeen built on σ-algebras. Later the Individual ergodictheorem was studied on more general structures like MV-algebrasand quantum structures. The aim of this paper is to formulate theIndividual ergodic theorem for intuitionistic fuzzy observablesusing  m-almost everywhere convergence, where  m...

Vibration of Road Vehicles with Non linear Suspensions

In order to investigate the effects of non-linear springs in vibrating behavior of vehicles, the independent suspension of conventional vehicles could be modeled as a non-linear single degree of freedom system. The equation of motion for the system would be a non-linear third order ordinary differential equation, when considering the elasticity of rubber bushings in joints of shock absorber. It...

Multiple Recurrence and Finding Patterns in Dense Sets

Szemerédi’s Theorem asserts that any positive-density subset of the integers must contain arbitrarily long arithmetic progressions. It is one of the central results of additive combinatorics. After Szemeredi’s original combinatorial proof, Furstenberg noticed the equivalence of this result to a new phenomenon in ergodic theory that he called ‘multiple recurrence’. Furstenberg then developed som...