grandes-ecoles 2022 Q49

grandes-ecoles · France · centrale-maths1__official Proof Proof of Equivalence or Logical Relationship Between Conditions

Prove the linear non-squeezing theorem: For $R > 0$ and $R ^ { \prime } > 0$, there exists $\psi \in \operatorname { Symp } _ { b _ { s } } \left( \mathbb { R } ^ { 2 m } \right)$ such that $\psi \left( B ^ { 2 m } ( R ) \right) \subset Z ^ { 2 m } \left( R ^ { \prime } \right)$ if and only if $R \leqslant R ^ { \prime }$.

Prove the linear non-squeezing theorem: For $R > 0$ and $R ^ { \prime } > 0$, there exists $\psi \in \operatorname { Symp } _ { b _ { s } } \left( \mathbb { R } ^ { 2 m } \right)$ such that $\psi \left( B ^ { 2 m } ( R ) \right) \subset Z ^ { 2 m } \left( R ^ { \prime } \right)$ if and only if $R \leqslant R ^ { \prime }$.

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