Lecture

Volume Growth of Positive Contactomorphisms

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Description

This lecture discusses the growth of positive contactomorphisms in terms of Legendrian spheres, Lagrangian structures, and symplectic forms. The instructor explains the notation and the growth of f functions, providing theorems and topological conditions related to the topic.

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Related concepts (32)

Symplectic vector space

In mathematics, a symplectic vector space is a vector space V over a field F (for example the real numbers R) equipped with a symplectic bilinear form. A symplectic bilinear form is a mapping ω : V × V → F that is Bilinear Linear in each argument separately; Alternating ω(v, v) = 0 holds for all v ∈ V; and Non-degenerate ω(u, v) = 0 for all v ∈ V implies that u = 0. If the underlying field has characteristic not 2, alternation is equivalent to skew-symmetry. If the characteristic is 2, the skew-symmetry is implied by, but does not imply alternation.

Symplectic manifold

In differential geometry, a subject of mathematics, a symplectic manifold is a smooth manifold, , equipped with a closed nondegenerate differential 2-form , called the symplectic form. The study of symplectic manifolds is called symplectic geometry or symplectic topology. Symplectic manifolds arise naturally in abstract formulations of classical mechanics and analytical mechanics as the cotangent bundles of manifolds.

Chord (music)

A chord, in music, is any harmonic set of pitches/frequencies consisting of multiple notes (also called "pitches") that are heard as if sounding simultaneously. For many practical and theoretical purposes, arpeggios and other types of broken chords (in which the chord tones are not sounded simultaneously) may also be considered as chords in the right musical context. In tonal Western classical music (music with a tonic key or "home key"), the most frequently encountered chords are triads, so called because they consist of three distinct notes: the root note, and intervals of a third and a fifth above the root note.

Extended chord

In music, extended chords are certain chords (built from thirds) or triads with notes extended, or added, beyond the seventh. Ninth, eleventh, and thirteenth chords are extended chords. The thirteenth is the farthest extension diatonically possible as, by that point, all seven tonal degrees are represented within the chord (the next extension, the fifteenth, is the same as the root of the chord). In practice however, extended chords do not typically use all the chord members; when it is not altered, the fifth is often omitted, as are notes between the seventh and the highest note (i.

Barre chord

In music, a barre chord (also spelled bar chord) is a type of chord on a guitar or other stringed instrument played by using one finger to press down multiple strings across a single fret of the fingerboard (like a bar pressing down the strings). Players often use this chording technique to play a chord that is not restricted by the tones of the guitar's open strings. For instance, if a guitar is tuned to regular concert pitch, with the open strings being E, A, D, G, B, E (from low to high), open chords must be based on one or more of these notes.

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