We study the problem of coexistence of a countable number of periodic orbits of different topological types (saddles, saddle–centers, and elliptic) in the case of four-dimensional symplectic diffeomorphisms with a homoclinic trajectory to a saddle–focus fixed point.

There exist two different types of equilibrium points in 3-D autonomous systems, named as saddle foci of index 1 and index 2, which are crucial for chaos generation. Although saddle foci of index 2 have been usually applied for creating double-scroll or double-wing chaotic attractors, saddle foci of index 1 are further considered for chaos generation in this paper. A novel approach for construc...

Common causes of poor performance in horses include factors related to the horse, the rider and/or the saddle, and their interrelationships remain challenging to determine. Horse-related factors (such as thoracolumbar region pain and/or lameness), rider-related factors (such as crookedness, inability to ride in rhythm with the horse, inability to work the horse in a correct frame to improve cor...

investigating the frequency of traumatic nasal bone fracture in patients with and without old septal deviation and possible deviation. prospective study of 105 patients with nose trauma conducted and cases were divided into two groups: a study group 35 patients with nasal fracture and a control group of 70 patients without nasal fracture. diagnosis of septal condition was made by anterior rhino...

Saddle point search on an energy surface has broad applications in fields like materials science, physics, chemistry, and biology. In this paper, we present the shrinking dimer dynamics (SDD), a dynamic system which can be applied to locate a transition state on an energy surface corresponding to an index-1 saddle point where the Hessian has a negative eigenvalue. By searching for the saddle po...

BACKGROUND As dental implants receive masticatory stress, the distribution of stress is very important to peri-implant bone homeostasis and implant survival. In this report, we created a saddle-type implant and analyzed its stability and ability to distribute stress to the surrounding bone. METHODS The implants were designed as a saddle-type implant (SI) that wrapped around the alveolar bone,...